Well In a personal opinion I will say a lot of stuff that I found both interesting and disappointing in these games,much of this is my personal opinion and in fact I think that is down to what people like in a racing game,so here goes:
Pro:
-In Forza 3:
*Better damage system.
*More "interactive AI" when is set to hard.
*Paint your car,and apply liveries(I'm don't really like this but a lot of people do).
*A slightly better car selection(more lambos and Porsche).
*Better body kits and ore variety when customizing(Again I don't like this).
*Matchmaking or racemaking system.
*Some nice tracks like Fujimi Kaido.
*cockpit view in all cars.
-In GT5:
*Track with Day/night transition and weather.
*Rally stages.
*More Racing categories like some F1 racing as well karting and NASCAR(I don't like nascar but I think some do like that left turn based racing).
*Track Creator(or track random creator,something that I really like).
*More graphics in the important cars and tracks.
*1000 cars(I know about standards but since there are like 700 cars without the variations of the same car that is a pretty good number of different drivable models,even if they don't have cockpits).
*Photo travel mode.
*Special events.
*Better physics,and better feel of the game overall.
*Better overall online mode.
*More tracks(I say this because in FM3 there is like 8 tracks based on the same location,in example ladera test track and monserrat,which are advertised as different locations but at the end is the same track).
*(personally)A harder game(earning credits in FM3 is a joke).
*More cars while racing.
*Play free online.
Cont:
-In FM3:
*The rewind function(something that I personally hate,this makes online players more stupid and childish when racing,besides it takes all the challenge that racing represents,this for me is a cont,this feature was introduced by Grid and had restrictions,but the unrestricted rewind function just spoils the challenge that AI manages to give you).
*Replays,the replay are not that good looking,I know that you can see a lot of cameras but the main one is just awful unfortunately)
*Graphics and brightness(FM3 nurburgring looks to dark and unfriendly,like nurburgring wasteland, don't like it at all,also cockpits are not well textured,they are not at the same level of Dirt or GT in that aspect).
*Lack of tracks and lack of city tracks as well night tracks.
*DLC,if you want a good updated version of the game it will cost you at least $20 in DLC alone,something that will probably will happen with GT5.
*lack of variety in races.
*Loading times(nurburgring takes about 1:30 to load,as well some slowing down when loading cars on the dealerships).
*Lack of original tracks(just 2 new addition in the tracks selection,and Le Mans doesn't look good).
*Lack of other motor sports like rally.
*Also the online mode which is a joke compared to what they did on FM2.
*Physics overall are plagued with flaws such as 2WD cars converted into 4WD cars?,Is good to see this in cars like skylines and Japanese tuning cars but an Italian F430 4WD,forget it,cars lost a lot their identity.
*Lack of cars while racing I'm fine with 10,but they cant do that.
*Endurance races,which are just a long arcade race with a mandatory pit stop,is not as dynamic as GT5 and lacks a lot of things like a animated pit crew,which gives you a lot of sense of realism.
*The In-car issue,yes FM3 has almost 550 cars with cockpits,but the driver looks really bad,no much of the interior can be seen from outside and the whole game reduces resolution while on race,I know this because that loading time while entering in photomode is to load the details that the players should be looking at while racing.
*Finally the lack of exporting images to others formats and other devices,that really hurts photomode.
-GT5:
*700 standards(they drive as they should,but they don't look as they should,very disappointing there).
*Lack of livery.
*Damage(I mean Lv 20 but still not as good as FM3 does).
*lack of original tracks(probably been saved for DLC).
*Very poor Body kits and customisation overall.
*The levelling system.
*Mandatory B spec.
My point is simple,if you like to tune your car,make it look good and expend your time in making the car looks gorgeous then go to FM3,also FM3 is easier but if you like to drive the cars,really drive them and play with them go with GT,maybe the AI is not that good,but the concentration required to complete races is something really entertaining,and the physics work really well with all cars even with standards so GT5 is more of a driver's game,as you can see I take GT5 over FM3 because of the driving,I rather waste my time racing in nurburgring than building a car with Rei or Asuka on it,I do, is just how I am.
And I found online in GT5 much more entertaining,people are more skilled and while there is no damage(well there is thanks to an update)people race very well and they enjoy themselves,so is up to you to decide what you like the most,some say that you should have both,I say you should have both if you can,having two games and two systems is not bad,but see some features in one game,while the other one doesn't have it can be disappointing,so is all down to what you like that is all But MY personal opinion is that GT5 is way better,but because of the reasons that I just explain.
Edit:I like FM2 over FM3,had better physics and the online in that one was terrific.