Erik, it does play differently, because the tee shot is coming from an angle that makes the fairway feel much wider. When you stand on the tee, everything to the right looks like fairway, even though you know that if you bail out that way you can go through the fairway and get into trouble, whether bunker or OB. But without the tree, the fairway is effectively very wide, because you're playing more of a "cape style" (don't come at me, y'all, I know it's not really a cape hole) tee shot, not one where you're lined up and driving between the ocean and the bunkers. This picture, which shows the old location of the trees, gives you an idea of the visual.
Without the tree, it's actually not a very intimidating drive, if you're a decent driver of the ball. If you take it on a line where the trees are (but assume they're gone), so just left of where the last fairway bunker is, you don't have to even carry very much ocean (around 170 yards, per Google), and the fairway doesn't run out until 295 so you can really bang a drive and have a chance to attack the hole while taking a pretty safe line (you're biggest threat would be that a slight push would find the bunker). Really you can just stand on the tee aim just left of the bunker and if you can make a swing that eliminates a pull, you're golden.
The tree(s) make that a lot more dicey, as you can see. You have to either hit a drive that draws, or take a line that carries a lot more of the coast and has a lot less room for error in terms of a pull.
It's not that anyone plays the hole by deliberately trying to play right of the tree. If you're playing it as a three shot hole, you tend to play a drive that's well shirt of the tree and it's not an issue on the second shot at all (see Phil with an iron off the tee on Monday morning). What the tree really does is ensure that if you're driving to be aggressive, you have to hit a good aggressive drive up the left side to be rewarded with a good chance. If you bail right, you don't get away with it (but you'll styill have a shot and be able to reach the green in 3--maybe even 2 if you're Tiger in 2010).