Hi!
You've already noticed some of the differences (and that's good), so you can start working on them.
First, can you set your axes to be separate? It is important, but you can still make progress as it is.
Sets can differ a lot, as probably yours and the WR holder's aren't the same, so braking force may differ too

. Don't take notice on how long you both brake on that spot, try to brake a bit less than that and you'll be able to enter the corner at desirable speed. But carrying that speed through the corner is another issue and it depends a lot on the set. Sets for AS3 for most cars are very specific, since the preferable thing is to use very little downforce and rely on mechanical grip only. It is very hard to make a good AS3 set that will be competitive with all the guys who know a lot about car physics. Furthermore, even if you take the WR set doesn't mean you'll be able to drive it close to WR times. You need to practice a lot and crash dozens of cars to get the feeling which is the best and fastest way to drive through the whole track.
What wheel do you use? If it shows movements on the straights, even if you don't move your wheel, it looks like the pot in the wheel is dieing... and yes, all those small movements slow the car a bit and make you lose some time. Also, if it is so, it's not precise enough in the corners and that loses you more precious time.
So, yes... probably the time to buy a new wheel
