Like Hiroshi says, he hasn't posted this thread to start a flame war, so I'll post my initial comparisons (since becoming an XBOX360 owner on 22nd Oct and Forza 4 being the first of the series I've ever driven).
I'm a long time Playstation user (PSX, PS2 and PS3) and have played all the GT series right up to GT5. I have to say that whilst I enjoyed GT5 it wasn't quite what I was expecting, especially after 5 plus years of development. Had its pro's and con's just like any game, but for me it wasn't really the great leap I hoped for from GT4.
Playing Forza 4 has so far been an enjoyable experience and whilst I was never a Polyphony fanboy and one to rubbish the Forza franchise, it has been nice to see things from the other side. Here's a brief overview of some areas of F4/GT5......
To compare both titles, I would have to say the cars feel better in F4 than they do in GT5. I feel I get better feedback through the pad in F4 than I do in GT5 and can make the steering adjustments required much easier.
I think F4 just takes in on the sound of the cars too, though there's not a vast gulf in sound difference, although the lame crash sound effect in GT5 was a let down (sounded like hitting a wheelie bin, lol).
Car modifications I would definitely say again F4 has the edge, especially in the car painting and upgrade department.
F4's tracks are good, and the real life replications are excellent. GT5 would take this one for me, just because of the track editor, which although is limited in it what it allows the user to create, its a track creator all the same. Polyphony also brought along some of the classic older GT fantasy tracks, but lwt me down a little as I expected GT5 to bring all the back catalogue of tracks to the table, which it didn't, so we are still missing some of the old favourites.
Graphically, I feel there isn't oo much betwen the titles. Both have a very good photo mode, although GT5 seems to allow the user a wider variety of locale. Car recreations in both titles are excellent, though again GT5 lets itself down slightly with the 'standard' models, as they are basically ports from GT4 and not HD models, though there have been around 200 getting the 'premium' updated spit and polish.
Interior cockpit views in bith games are again very well done, but once more Polyphony dropped the ball by not having all cars with interior cockpit view, and the standard ones that didn't have it, now have the very poor silhouette cockipt template, which doesn't inspire me at all.
F4 has a better structured career path mode, where in GT5 you just attain the appropriate licenses and pick and choose your race series, so not exactly a structured career mode. I think F4 made a good move with how you receive gift cars for attaining level ups, where you can actually choose form a handful of cars, compared to GT5 where you are stuck with the car they award for passing a certain license.
Both have the usual online marketplace where cars can eb bought/sold/shared, so even stevens here.
As for online connectivity, both allow the usual lobby match-ups and group races, but I feel F4 caters more for the club element of both games. One feature I did like was that when you join a club, the game prefixes your exisiting gamertag with the club tag, whereas in GT5 you would have to create a new user profile with the appropriate club prefix, but this may be down to the PSN and not solely GT5.
Finally, F4 wins hands down with its Rivals fetaure. Similar to EA's Autolog feature, you can happily hotlap to your hearts content whilst knowing you are also competing for positions on the leaderboard amongst friends, club memebrs and the rest of the world. Whilst Gt5 has laptime leaderboards, there is no interaction like you get with Rivals.
If you have ended up reading all of the above, I presume by now you will have worked out that for me, F4 comes out as the winner in the comparison stakes. It has also taken top billing as the PS3 is currently unplugged and sat in a corner, licking its wounds, although Uncharted 3: Drake's Deception will soon see it receiving some gaming love, lol.
To convey my comparison opinions for both games (and yes, they are my opinions and not something everyone has to agree with or take as read) in football terms, I would give F4 the 3-1 victory.
Foot to the floor and happy driving.