They're both great subs and you couldn't go wrong with either one, but if I had to pick between the two I'd go with the Infinity cuz it has the traditional round design (easier to find a box and just my personal preference) and the ideal recommended enclosure volume is a lil bit smaller than that for the kicker. 1 cu. ft. vs. 1.44 cu. ft. --not very big a difference but everything else being equal the size may be, for you, the deciding factor. These of course are just specs. and they're so close that adding a lil polyfill could even it out so don't go by just that.
Something to think about depending on what kind of amp you have or are planning to get: The kickers are only available as a DVC sub (both a 4-ohm voice coil version and a 2-ohm voice coil version). The infinity's can be DVC (4-ohm coils only) or just the single 4-ohm voice coil.
Also obviously the kickers are square and it is usually harder to find a box with a square cutout; when you can find one they're almost always more expensive than their round-cutout equivalent. However, you can often buy a round-cutout box and cut the corners to make it in to a square cutout box if you're a do it yourself type person.
I've heard both subs in small sealed boxes, and I've also heard the infinitys in a ported box. The infinity's definitely go a lil deeper although you can barely even tell most of the time since we're talking 25 Hz and below. Both handle power really well and both seem to hold up pretty well from what I've seen. Also I don't know if it's important to you or not but the infinitys have a 3-year warranty which by industry standards is pretty lengthy.
I know they always promoted the infinity's to be sort of a bridge between an spl sub and an sq sub--i.e. something that'll go deep and loud but will be clear throughout. From what I've heard out of them, I can definitely say they accomplish this quite well. To be fair though, the kickers are great subs too and they can pound like a mofo . I should mention that most people agree the infinitys' RMS power ratings are quite underestimated. I have seen these subs pushed to 600 watts RMS for hours on end with no problem, so don't let the infinity's low RMS specs. scare you away.
People always have all sorts of different opinions and stories (good and bad) about certain brands or models to share with everyone else and I'm interested to see what others think about this. I must warn you though, there's always gonna be a few morons who wire up their subs wrong or try to push them with 50 watt amps while they distort like crazy and then after a week or so they tell everyone that those subs suck because they "blew so easily" or some other BS excuse.
You're gonna have people telling you that kickers are crap and infinity's rule; then you'll have people saying that infinity's are crap and kickers are the best, and it's kinda hard to know who to trust. That's why I say trust your own ears. If possible go to a local shop and listen to both subs. The kickers are a little easier to find in regular stores than the infinitys but you can find both brands online at places like crutchfield and soundomain. Crutchfield does do free return shipping if you're not happy with how they sound so keep that in mind too (if you're not able to listen to the infinitys in person beforehand). Usually I find the infinitys run anywhere from 15-75 bucks more than the L5s, so think about that too if your budget is tight.