Many of you have made some very poignant and well thought out posts on this topic.
By it's very nature as a console game, Gran Turismo has to be many things to many people. It has to be playable and accessible to an 8 year old, sitting on the couch with DS3 in hand for the first time. And it has to be equally enjoyable to legacy players who were weaned on GT1. And everything in between. Not an easy feat, being all things to all people.
By comparison, iRacing is much more focused. It's not a game. It's a true simulation. And you will never find paint chips or a B-spec mode in iRacing. Let alone, knocking over cones on the moon.
Having played both GT5P/GT5/GT6, as well as many other semi-sim racing titles on the PS3 (including Ferrari Challenge, Supercar Challenge, F1CE, Superstars of V8 Racing, etc), and GTR Evo, Race 07, Rfactor, LFS, iRacing and Assetto Corsa on the PC, I think the basic fundamental difference comes down to this.
GT is a game for car lovers and car enthusiasts. If you were ever delighted at recreating your own car virtually, or taking pictures in photo mode or playing around just so you could see the fireworks and then the sunrise at La Sarthe, or the idea of taking a Rally car or a Nascar onto the ring, just because, it's hard not to like GT.
iRacing is a sim for virtual racing fans. If you're a hard core Le Mans/ALMS/Rolex fan, who loves the competition and fancies a chance to go toe to toe with other racing drivers and maybe does the odd track day, you'll live iRacing.
That said, one can also like and enjoy both. In fact, right now, I find myself at odds with both games. I once ran a league in GT5. But the over-boosted slip stream, ridiculous tire model and limited 16 player connections began to frustrate me. I wanted a level of realism that GT5 simply couldn't give me. So I joined iRacing about 2 & 1/2 years ago. It was everything I'd hoped it would be and I managed to progress pretty well. But as my IR & SR went up, and my free time went down, I found it hard to keep up. Once you start racing in higher tiers with well supported series, if you don't show up with your A game and don't have the time to practice and find a good setup and really put down competitive times, well, simply put, you'll wish you hadn't.

There are no 'cruising' lobbies in iRacing.
So lacking the time to pursue my iRacing career, I bought GT6 really hoping for a good off-line game. A racing game I could pick up at any time without having to check series schedules and putting in an hour of practice just to cut 0.5 out of my time. And I think I can say, everything that was good about GT5 is better in GT6. The tire model is a step up. The slipstream is more realistic. Unfortunately, some things haven't improved. After working my way from novice through IB events, I've given up with career mode and just can't be bothered anymore. I just can't take the same, move from the back, conga line start, pass the leader in 3-5 lap affairs, that involve a bunch of truly hapless, slow moving, brake checking, door closing, throttle fearing dumbots, that serve no purpose other than keeping you from reaching the rabbit out front, that has bugger all to do with real racing. There I said it. Despite the limitations of the PS3's hardware, the PSN itself and the inherent connection problems, if you're looking for a virtual 'race', it's clear that with the right group of people, the online mode in GT6 is far better than anything in off line mode. Although, it's not the reason I bought it. And if I want a great online race, I have iRacing for that, where it's possible to race 40+ opponents with comparatively little lag. There's a benefit to having dedicated servers and in that sense, with iRacing, you get what you pay for.
So GT6 is a fun game for me and good for hot lapping and time trials and for those days when I come home late and I'm too tired to turn to iRacing. The physics in GT6 are indeed a step up, but anybody who wants to put it on the same level as iRacing or Assetto Corsa is fooling themselves. And I would venture to guess that 90% of the people who buy GT6 don't really want and don't really care about striving for ultimate realism. And that's just fine.
They're both driving simulations with a very different purpose and scope.