When I play as a medic I almost always use the medigun. In what situations is the Kritzkreig more useful?
First, you need to look at when the übercharge is useful: taking out entrenched engineer nests, and leading a strong push. This makes übercharge particularly useful for spearheading an assault.
On the other hand, the Kritzkrieg is useful for countering a push, because it lets someone push out a large amount of damage in a short span of time. Use the kritzkrieg to clear contested points, hunt down regrouping enemies, etc.
The Kritzkrieg also charges faster. If you're finding you often die before you get a chance to deploy an übercharge, you might try switching to the kritzkrieg, as you'll build up the kritz-über faster.
While the answer is situational. Lets cover the basics first:
*New in TF2 Beta, also speeds you up when healing a faster target, such as a Scout. However, it has no overheal, although you can continue healing targets to build your Übercharge.
Now for some scenarios:
So, the rule of thumb is to start with the Medigun if there are setup gates. Be aware that the walls can be jumped on cp_well. Use the Medigun to take down Sentry Guns. Kritzkrieg works well for pushes against sets of enemies that have no sentry farms. Quick Fix is still new and may be useful in one of these two situations, I haven't tested it enough to tell.
You already got some good answers, so I only add a point that could be useful and hasn't been mentioned yet.
Due to the fact that most servers have 24 slot or even 32 slots in order to have some chances to win your team usually needs at least two medics, sometimes three.
In this case having one medic with medigun and one with kritzkrieg guarantees good team flexibility. An übercharge used to destroy the sentryguns or the opponent heavy+medic duo followed by a kritzcharge could be extremely painful and could break stalemate situations.
The Kritzkreig leaves your target open to damage, making it less useful in games with many players (and a lot of damage going out). It works best on soldiers and demos, because they can do damage without getting close to the fight. Also, critical rockets and grenades quickly take out players surrounding a sentry, so the Kritzkreig uber will kill Engineers repairing sentries. The Medigun's uber will have a harder time killing engineers because there is no bonus damage against players.
Also, the Kritzkreig charges quicker than the Medigun. If you're losing or trying to take a capture point the Kritzkreig will both charge faster and provide more damage output to clear the point, especially on Soldiers and Demomen (once again).
In short: use the Kritzkreig for destroying big Engineer setups that you can fire at from a distance, or to clear capture points. Otherwise you will have better luck with the Medigun when you have enough time to charge it.
I'm not a competitive player myself, but I do believe I understand the theory behind competitive play reasonably well. Please correct any mistakes in the comments.
In competitive Control Point play, teams are limited to one Medic each. The team whose Medic is closer to being able to deploy an Ubercharge is said to have "Uber advantage". It is very difficult to stop a skilled, ubered team from capturing a point, so having Uber advantage is essential.
Imagine the opposing team reaches full Ubercharge first and pushes into your point. The worst possible outcome is if the team takes control of the point and kills your Medic in the process, since they will maintain Uber advantage (your Medic is dead while the opposing team is already building the next Uber).
If your Medic is reasonably close to a full Uber himself, the best option might be to force the opposing Medic to deploy Uber, but ultimately concede the point in order to protect your own Medic. Hopefully your own Medic will have Uber ready shortly after the point is taken, and you can immediately reclaim the point. Even better would be if you could reclaim the point and kill the enemy Medic, swinging the Uber advantage in your team's favor.
If your Medic has died recently and the opposing team has significant Uber advantage, you might want your Medic to spawn with Kritzkrieg (finally getting to your question). Since the Kritzkrieg charges much faster than the Medigun, you may be able to meet the opposing team's Uber with your own Kritz. This is particularly relevant if your team is defending their last control point, since conceding the point is not an option. If all goes well, Kritz will allow your team to get several one-hit kills against enemies that are not currently Ubered, decreasing their capping ability considerably. In the very best case, you will enjoy such an advantage in numbers that you can track down and kill the enemy Medic. If your team's Medic now switches back to Medigun, you will have successfully defended your point and regained Uber advantage, which is quite a spectacular play.
And now you have the Vaccinator as an option, so let's go over some good situations to use that Medigun in too.
The Vaccinator serves many of the same functions as the regular Medigun with its ability to reduce damage, but is especially effective at punishing a team that overinvests in a particular source of damage. Against 5 Soldiers, Explosive resistance can save a team's life. Against Snipers, bullet resistance can mean the difference between life and death.
Like I said before though, it can also serve as a reliable mini-uber, which means it is good for spearheading an assault. Bullet resistance works wonders against an engineer nest, and any type of resistance (against a type of damage the other team is using) is always helpful.
Another good use of the Vaccinator is when you find it difficult to build up an Uber, but badly need the help that a Medic's charge can provide. The mini-ubers that the Vaccinator builds up take very little time to charge, and you can split them out however you like to help your team.
That being said, it takes a lot of skill and a LOT of situational awareness to know what type of Mini-uber (or even what type of base resistance) to employ at any given time. So on a personal level, if you don't feel like you have that much situational awareness, or can't make that split-second decision on which resistance to use, then it might be better to use a regular Medigun or Quik-Fix.