Well, I prefer not using the Ascension Crystals, or the Tech Victory, and usually not the Influence Victory, just so I can stretch the game out. Here's some ideas of how these victories have translated for me in my games:
Keep in mind that these typically happen on the harder levels, a little above normal, and ofcourse the easy levels are not represtented here.
Ascension Crystals - The AIs will come at you hard and relatively fast in relation to how long it takes to achieve the points needed. Expect a game where at certain points and for long stretches the whole galaxy will seem to be at war with you. If you can win on Masochistic or above with this victory condition, then my hat is off to you!
Tech Victory - On larger maps, I have found that I am almost always behind technologically (though I play with Techtrade and stealing off to enhance the races' uniqueness) Obviously, I do not want the race on the farside of the map from me being able to win the game before I have a chance to tickle them. However, I have not found the AIs to come at me hard when I became close to winning technologically. This condition is obviously yet drastically affected by the research speed you set for everyone at the beginning of the game: Very Slow, Slow, Normal, Fast, Very Fast.
Influence Victory - On smaller maps with certain AI's this can be the quickest way for me to lose. It can also be one of the quickest ways to win if you specialize in influence and diplomacy tactics. On large maps, I did not have a problem with losing fast, but it does preclude you from conquering every one since the game ends when you control 75 percent of the map. (for ten turns I think)
Alliance Victory - I leave this on only as a way out of games I am both dominant in but do not have the patience or motivation to finish off with a conquest. The AI's can not beat you by them using this condition since you simply do not ally yourself with someone who is allied with the rest of the galaxy

But it can be an easy way to satisfactorily complete a game so you can begin the next challenge.
I like going for conquest in a long and epic game. Often times the real fun begins for me when most races have the tech trees researched. I avoid those conditions that end the game prematurely for me so I usually play only conquest/alliance conditions.