The medigun is almost always what you should be using, because the invuln uber is irreplacable and almost game changing; the smaller number of players you need to keep alive (in constrast to the 24/32 pub servers) means that every life counts, so it makes sense to use it.
The kritzkrieg can and should be used a) if the opponent is not expecting it (although this can’t always be judged accurately), b) if you feel like a change of gameplay, or c) if your demoman is especially competant with sticky aim. True to its naming roots, it’s a very quick and aggressive surprise attack; the 25% increase in uber rate means that if a team isn’t expecting it, the sudden pop and crit advantage on a demoman is absolutely huge, to the point where entire, only slightly bunched up teams can be wiped. The counter to the kritz is keeping a fair distance and running away – of course, this is a lot easier if there is prior knowledge of its use, emphasising that this is a surprise tool to use against an unaware opponent. To this end, the medic should hide the kritz as much as possible while still performing heals. After a number of uses, a switch back to the normal medigun is advised, as the enemy will expect and will prepare for kritz, perhaps putting them out of position. The kritz is also advised for use if you have the uber advantage, as there will be no counter invuln to stop you. Be wary of increased medic targetting if using the kritz.
The quick fix. To the best of my knowledge, the quick-fix is banned in most leagues; for that matter, there is absolutely no reason to use it – the loss of overheal is a massive disadvantage – handicapped demo rollouts is a huge loss, as without the overheal the demoman will be unable to reach the midpoint without significant damage or speed loss. On top of that, the uber is sub-par compared to the normal medigun. Avoid at all costs.
Tl;dr kritzkrieg if you have uber advantage or element of surprise, otherwise use medigun.