The game has to support 16:9, and unfortunately, many of them still do not.
HDTV Arcade is arguably the best and most accurate source on which do what, so I definitely recommend checking it out and comparing it against your collection.
Concerning which you should get, well, there are pro's and con's on both sides of the fence, but ultimately, I think it boils down to how long you plan on keeping it and which shortcomings you find more bothersome. It's pretty basic really, the 40" is larger, sports a lower resolution tube (tell'em about it Thump), and will feature the traditional, horizontal black letterboxes on HD and DVD content. The 34" is smaller, has the higher resolution tube, and will feature your choice of stretched 4:3 content (disproportioned), or vertical, black letterboxes (with accurate -non stretched- proportions). Like I said, personal preference.
If Microsoft is to deliver on their promise that the PS3 will not enjoy the head-start of the PS2, Old Man Xbox has probably only got a couple years kick left in it (assuming you teeter on the cutting edge of console gaming). It really doesn't take a soothsayer to predict that the next crop of consoles will be pumping out HD - 16:9 with every major release, it's an inevitability. All bets are welcome. If this is a long term investment, I always recommend you take that into consideration, but if the letterboxes of the 40" don't bother you, it probably won't be to big of a deal.
Anyways, good luck, happy shopping, and make sure you sniff out a good deal!