I'm currently just trying to finish out off the challenges available pre-prestige, but am wondering if anyone out there has any experience doing this after prestiging, and whether it seems earier to do while going through the weapons-unlocking again.
You don't gain a real advantage after prestiging that would make challenges easier, so I don't think it would matter when you choose to do them (Aside from losing progress, but if you haven't gotten that far, it shouldn't matter).
Personally, I do the challenges after prestiging (if I even choose to), because unlocking the same weapons over again is boring to me and the challenges keep it fun.
I'm on 8th prestige at the moment, and here are some thoughts:
It's tough to lose all your weapons and perks (losing Ninja Pro is painful)! IMO it's always tough to get all your stuff back and finish off challenges after entering prestige, because you'll always think to yourself: "Hey, I've done this before! Why did it just said... Oh! That's because I've entered prestige..."
Having said that, there are certain challenges that are easy to get (they tend to be the ones that are available from the get-go) and some that are the complete opposite (such as dropping a crate to an enemy)! But, when you do prestige, at least you'll have some idea how to do those challenges.
Well, one thing is that after completing 70 levels you've got the experience to make it that much easier to go through again. You don't have to relearn the maps, you know strategies / campout locations, etc.
One good about prestiging is the extra class you get. While not all that useful immediately it is nice when you re-unlock One Man Army.
On the flip side (in my own personal opinion) I'm reluctant to prestige as I prefer the sniper rifles. You just don't get the kills while sniping that you do in close combat. Takes longer to progress. Could be that I just suck, though :)
As squillman mentioned, you receive an extra class every odd level prestige. Also, there are extra challenges available for each type of weapon and kill streaks once you prestige for the first time.
I am currently fifth prestige, and I usually completed one type of master challenge per weapon type (SMG, Assault rifle, sniper rifle and LMG). So at one time, I had a class dedicated to a SMG, Assault rifle and LMG. I have completed all of the SMG master challenges. I only need to complete the M240 master challenge for the LMGs. The f2000 and AK47 master challenge for assault rifle challenges. The WA2000 and M21 EBR for sniper rifle challenges.