Warning: essay-length answer ahead.
I'm going to start off with a "disclaimer" just so you know what perspective I'm coming from:
I used to take these games very seriously. I was a staff member on the largest GH/RB website, and I suppose you could technically call me a "professional", since I won several thousand dollars worth of cash/stuff playing these games. You should also note that I used the past tense for that statement. I've been out of touch from the community for close to two years now, so I don't know anything about any of the Guitar Hero series after World Tour, though I have played a fair amount of Rock Band 3, which should reveal my preference between the two series. This preference is going to be pretty apparent in my answers. Spoilers: I'm going to heavily recommend RB3.
First of all, I think a bit of history of the two series is in order. The first Guitar Hero game was a collaboration between Harmonix (on the software side) and Red Octane (on the hardware side). The same team created Guitar Hero 2, as well as the 80s game, which uses effectively the same engine as GH2. At this point, paths diverge. Activision purchased the GH franchise from Harmonix and handed it off to Neversoft to take over development. Neversoft's first game in the series was GH3, which, though having mostly similar gameplay to GH2, was a from-scratch engine rewrite. Red Octane went along with the GH name, and carried on to continue creating hardware for that series. Harmonix, no longer able to create "Guitar Hero" games, came up with Rock Band, extending the game out to include drums and vocals, and having to engage a different manufacturer for their peripherals (I think it was MadCatz, but I don't recall if MadCatz has been involved with RB since the very first game). GH responded with World Tour, adding the same instruments to their franchise, and from that point onwards the two series have basically been differently-implemented versions of the same underlying game concept.
The result of this whole mess is that the RB games are generally considered to have superior software, but the GH games have superior hardware. RB's engine and interface generally show a lot more polish and thought than GH's does, with each iteration of the series further improving things.
What are the primary differences between Guitar Hero and Rockband with regards to the learning curve?
I can't answer this question with actual personal experience, since I went through the learning phase during GH2, so the RB series did not even yet exist. Both series have a fairly reasonable learning curve though, since every song can be played on four different difficulties: Easy, Medium, Hard, or Expert, with the chart becoming increasingly complex as you move up. All songs are also given a difficulty ranking, so there is a large range of different song difficulties inside each discrete difficulty level. Both games also have a Practice mode where you can pick a particular section of a song to play and even slow it down, which can help if you're stuck on something. However, my opinion is that the RB series (especially RB3) has a much better learning curve for a few reasons.
In every game except RB3, when playing on Easy, only 3 buttons on the guitar (green, red, yellow) are used. Medium added the fourth button (blue), and Hard added the fifth (orange). The result is that you do not have to learn to move your hand back and forth until you have reached Hard. However, RB3 has recently changed this, adding the orange button to some Medium songs (I am not sure if they also added blue to Easy). This is an improvement, because an increase in difficulty also tends to add a lot more notes to the chart. This made the Medium-to-Hard jump by far the most difficult part of the learning curve, since not only did you have to learn how to move your hand back and forth to hit the orange notes, but there were also a lot more notes to hit, and many of the previously-single notes were also turned into "chords" (having to hold two buttons at once). Moving the introduction of orange notes down to Medium smoothes the curve out considerably, since you can learn to move your hand while the chart is still relatively simple.
RB3 also eases the experience of failing a song quite a bit. Normally, if you fail a song, you have to restart from the beginning, which can be a pretty frustrating experience if you failed fairly late in the song. RB3 added a "continue" option which at least lets you play out the rest of the song (though your score won't count, and you won't be considered to have passed it). It also has easy access to a "no fail" mode, in case you want to attempt playing difficult songs without having to worry about failing out. This option is also quite easy to access in RB2 and some of the GH games though, so this isn't unique to RB3.
I'd also recommend learning on the RB series simply because of the ridiculous amount of downloadable songs that are available. The game is just plain going to be more fun to play if you can find a lot of songs you like and enjoy playing. RB has so many DLC songs that you have literally hundreds of options to pick from at every difficulty level. It'll cost you some extra money, but you can make the game a lot more enjoyable for your personal musical tastes by adding DLC. Playing songs you like repeatedly on different difficulties as your skill increases is going to be a lot more enjoyable than songs you dislike.
At a more advanced level, RB's hammer-on/pull-off system (which lets you play a sequence of notes with only one strum) and their strumming system are a lot more precise than GH's, which encourages you to learn to play more accurately. I don't know if GH ever fixed this, but their old HO/PO system around the time of GH3 used to allow you to "flail" wildly, and as long as you hit the right note as part of your flailing, you would be fine. However, in RB, you had to hit the right note and only the right note, or your HO/PO sequence was broken.
With regards to the Guitar Hero series (since the series has multiple titles under it), which title is the easiest for a beginner?
As I said, I'm not very familiar with the newer GH versions, I gave up on the franchise a long time ago. All of them should be fairly similar though, so if you want to go with a GH game, you may just want to look for the one with the most appealing song list to you.
Same as the 2nd question, but regarding the Rockband series.
RB3 is definitely the best version of the series so far, and it's possible to import (almost) all of the songs from RB and RB2 into it, so there's not really any reason to even look at the older versions any more. The only caveat is that they seem to have made it a little easier to fail in RB3, but they've also increased the amount of overdrive (which makes it easier to survive hard sections), so between that and the "continue" option I mentioned earlier, it shouldn't be a concern.
I realize that the GH games have evolved from the first one to the latest one and that you can't use the same guitar for all of them [...]. Should this factor in on my decision as to which series to play?
This actually shouldn't be true. I'm still using the guitar from GH3 as my main guitar, and as far as I know, it's capable of playing every GH and RB game perfectly fine. They have added some optional things to the different guitars over the series' lifespans, such as the "solo buttons" on the RB guitars, and the awful "touch strip" on the GH guitars, but these aren't necessary at all. In fact, most high-end players of the games hate these additional "features" and completely avoid using them. I would recommend getting a guitar from one of the GH games though, as opposed to one of the RB ones. I don't know about the RB3 guitar, but as of RB2 the GH ones had always been superior. You can probably find guitar controllers in near-perfect condition for sale on Kijiji/Craigslist/eBay, since the popularity of these games has been dropping off lately, and a lot of people are probably getting rid of the big instrument peripherals cluttering up their closets.
If you do decide to get into drums, you have to be more careful. RB went with a 4-drum layout (all "pads"), but GH decided to do 5-drum, with three "pads" and two "cymbals". Because of this, the GH controller does not work particularly well for RB, and vice versa. They're both supported both ways, but it can be a little awkward sometimes. Getting the correct controller for your chosen series is definitely best.
Has Rockband evolved in the same way that GH has, or in other words, does one have to purchase different versions of the instruments depending upon which title you purchase?
As above, this hasn't really happened, so you shouldn't have to worry about it. RB3 does have "Pro Mode", but Guitar/Bass require a completely different controller for that, which is actually a real electric guitar (not available until March), and Pro drums requires a 3-cymbal addon pack that's compatible with newer RB drumsets, but not the drumset from RB1. The RB2 drumset was quite a bit superior to the RB1 one anyway, so there's not really any reason you should be looking at an RB1 set regardless.
Phew. That was a lot. Let me know if you have any more questions and I'll try to answer them.
tl;dr: Buy RB3.