Another point of comparison for controller vs wheel - I took the console and controller to the living room to try it out with the 46" TV in there, so I could see if I preferred the theoretically correct FoV I could achieve there. I also tried it with the same FoV as my wheel setup.
I found with both FoVs that I mostly felt much more in control of the car with the controller, however my times weren't faster. I did race B qualifying, running around 20 laps, and my best was 1:40.1, whereas I've done 1:39.9 with the wheel, so it was very close. The main differences I noticed, going back from the wheel to the controller were:
1. Control of speed is much easier with the controller than the wheel. The short travel of the triggers vs pedals means you can adjust in timescales that simply aren't achievable with pedals. With the wheel, I feel for much of the time like I'm moving at the wrong speed, I'm either going too fast or too slow, but I can't make fast and accurate adjustments with the pedals. You either get it right first time or you live with it with pedals, but with the controller you have fine ultra fast adjustment. For that reason there were parts of the track that I struggle with a lot with the wheel that were much easier to get right with the controller.
2. For the low speed tight corners, which there are plenty of at Interlagos, the controller makes it massively easier to steer, as you just move the stick fully across, you don't have to constantly seek out the right amount of input device movement to maximise turning. So the technique is to keep the stick fully over, and modulate brake and throttle to adjust line. Again, I felt like I was much more accurate in those corners.
3. Physical effort is reduced, and I felt this freed my brainpower up to focus more on the actual driving.
4. Where the wheel totally wins is when you are at full throttle and want to steer by less than full movement of the controller stick. There's no contest there, the wheel is far superior. This is why in the current Forza 7 monthly rivals, which is an IndyCar around an oval, I was top 12% with a controller, then did a lot of moving about of the Xbox and cables to try it with the wheel, and was top <0.1% with the wheel, you just scrub so much less speed off with the wheel, which of course is why people find the wheel better for tyre wear in GT Sport.
BUT, as I said, despite feeling in so many places like I was doing better with the controller, my times weren't faster, they were a touch slower.