Relatively speaking, the 4-3 is a better run defense and the 3-4 is a better pass defense.
Now, that isn't saying that one can't do the other, but the schemes make it easier to accomplish one or the other.

The main difference between the two schemes is at the interior gaps of the offensive line. The 4-3 defense has a lineman for every gap. Whereas the 3-4 requires the nose tackle to have a two-gap responsibly. Now, this is where the personnel becomes an issue. It's hard to find an elite NT. The NT has to keep the lineman off of the linebackers and free them up to make plays. If the center/guard can get to the second level freely, the offense will have pretty good success running unless the defense commits extra men to focus on the A/B gaps.
The positive aspect of the 3-4 is that you can put more versatile players on the field. You are trading a DT for a LB. Therefore, better coverage, better blitz packages, and more flexibility in the game plan (if you can stop the run).

The 4-3 is a little nuanced in that the DCo can ask the line to eat blocks and have the LBs play sound gap assignments... Or he can free them up to be playmakers and be disruptive in the backfield. A lot of this depends on both personnel and down/distance. The key position in the 4-3 is the MIddle LB. LSU fans see the difference Beckwith had on the effectiveness of the defense. Just that one position (like the 3-4 NT) makes a huge difference.

So when choosing between the two, modern coaches face several factors:
1) can you get the personnel to run it.
- for the most part... Yes. Unlike the NFL where there are only a handful of guys that can perform at that level, college has enough talent to make it viable.

2) what kind of offenses do you face.
- with the increased popularity of the spread, the need to be better in coverage is starting to outweigh the need to slow down a power run game. More people away from the LoS and crowding passing lanes helps.

3)how are they going to handle the hurry-up.
- it's a lot easier to get OLBs off the field for a rest than DTs.

Both systems work, but lsu just might have decided they like the mix of pros and cons better at the 3-4 than the 4-3.
The saints have recently decided to do the same thing. It's becoming a passing game.