Kent,
First off,

!
If you are trying to decide between Resistance:Fall of Man and Rainbow Six Vegas, let me offer you a little insight into both. But before I do that, I need to preface this with a little disclaimer. I have not played Rainbow Six Vegas online and I have not played RFoM a whole lot yet.
RFoM is a little more on the run and gun side of things when it comes to FPSs. It does not have a cover system, a la Gears of War or GRAW. None of the weapons are real and each one is very unique; also each weapon has two different firing modes. By this I mean, each a something special about them. The carbine you start the game with has a 40mm grenade launcher attached to it and a pretty effective one at that. The second weapon you obtain is the Bullseye and its secondary function shoots out a homing tag. If you manage to tag an enemy with it, then your bullets home in on the enemy. I have not extensively used it, but it seems like it could be really useful. Other than those two, I have not used many of the other weapons. I have used the shotgun and the rocket launcher and they are both fun. The shotgun can be fired with one barrel or both barrels simultaneously, which means it packs a helluva punch if you get hit with it. The rocket launcher is fun in that its second mode causes the rocket you just fired to hold in the air and then you can direct it to where you want it. I am sure I missed a whole lot, but like I said I have only played the game for a little bit.
Now RSV on the other hand, I have played a great amount, as I had it on 360 when I still had the 360 and played through the single player campaign almost two times (did not have the time to finish it through a second time). I thoroughly enjoyed the game in single player, but did not have any online experience with it. RSV is a different type of FPS when compared to RFoM. RSV is a tactical type of game and requires some planning on your part when tackling areas of enemies. Cover is all but always recommended and required, otherwise the enemy will quickly kill you. A great majority of the time through the single player campaign you will have two fellow Rainbow Six soldiers with you to command around and give orders to. They are fairly smart and effective in their suppression of the various terrorists you will encounter. The enemy can be somewhat sneaky some of the time if you do not take the time to plan out your attack, though you do not have to be overly complex in your planning, just smart about it. The weapons in the game are based on current weapons in the world, with a good majority of them being on the cutting edge of design.
I would probably recommend picking up both of them. Though if you only want one for now, I would suggest going with the type of FPS you like better. Right now, I only have Resistance:Fall of Man, but am planning on picking up Rainbow Six Vegas sometime in the near future.
While I am at it, I will go ahead and tell you what I think of F1:CE with my limited playing time on it also. First off, if you have the DFP, then it will be set up to run in 200 degree mode which is vastly different than what is used in GT4. I am not used to it and every little input is picked up by the wheel. If you are going down a straight and you are not holding the wheel near perfectly straight, then the car will drift all over the straight, just like I imagine a real F1 car would do. The speed of the cars is unbelievable at first and you will most likely need to adjust to how fast corners come up. I started out at Monaco, as I know the track fairly well from GT4 and it was pretty difficult at first. I figure after spending a pretty good amount of time with the game, then I will be able to adjust and run some fairly respectable times.
Now all I need to do is play my PS3 more so I can give better reviews of Resistance:Fall of Man and Formula 1:Championship Edition.
Looking forward to playing online with you once you purchase a PS3 and I decide on a PSN-ID.

👍

And I hope I could be of some help.
Brett