Personally think DS4 and wheel are closely matched, wheel likely being slightly faster and probably easier to be fast consistently with due to the extra precision in control. Wheel main advantage probably being able to be more reactive with steering, controller you are a bit more of a passenger. Controller bigger advantage is likely for novice drivers who don't know correct approach to drive, the game helps you drive the correct way.
I think PDI have done a great balancing act, if controller did have a noticeable lap time advantage then it is odd that top 24 superstars in the championships seems to be mainly dominated by wheel users. People seem to use anything as an excuse, just try and improve driving technique instead. It is in a way a lot easier to drive fast than it is to drive slower. When driving quicker, car is working for you rather than against you and you know better what you are doing and what the car is doing. When driving slower, every corner might consistently be an adventure into the unknown.
How many known fast guys bothered to even put a qualifying time on the boards in the bus event?
As for GT3 at Suzuka... no way did a DS4 user get in the top 10, unless it was 5 minutes after the events changed and no fast wheel users had run any laps.
Your 'frustration' is caused by your lack of skill with a wheel than any advantage a DS4 user has. 2.00 laps in a GT3 car at Suzuka is at least 2-3 seconds off a fast wheel time (if I remember qualifying times correctly from the last time I ran GT3 at Suzi, fast laps are in the 57/58 range).
No way a DS4 user can trail brake as effectively as a competent wheel user... which is critical to braking as effectively as possible in to hairpins. And no way they can accelerate out as effectively either - you cannot apply partial throttle/steering with a DS4 anywhere near as effectively as you can with wheel/pedals... which is critical to fast exits.
Perhaps you should spend less time complaining about some perceived advantage DS4 users have and more time working on your wheel skills
Forget consistency, a wheel and pedals is just faster. By a significant margin.
Just because YOU can't brake as late/accelerate as early with a wheel compared to using a DS4 does not prove your point... Again, all this proves is your lack of skill with the wheel (as you say yourself - you're a novice wheel user), not a particular advantage with the DS4.
Unless you can you back up your claim that a DS4 can quicker than a properly fast wheel user? On any track or even a single corner? Maybe try downloading the FL ghost of a #1 time and run against it with your DS4... see how much faster you can go (or can't).
I can still beat you even with DS4, does that mean you are not a properly fast wheel user?

Think you are giving too much credit to wheel there but get the point you are trying to get across. At the end of the day, it is still running same physics, if one can hit the same lines then both should be quite close together. I remember giving Assetto Corsa on my laptop touchpad a go, I was amazed how well it went as I was able to be as fast as some of the top wheel drivers with the AWD cars. That brings me to the point that wheel is advantageous in being quick in every scenario rather than being more car/track combo dependent.
One thing that surprised me about this game since the closed Beta is how well it drives with a DS4 and the level of feedback, an incredible achievement. I never tried it at the Copper Box event with a pad thinking there is no point as I'm not very good on GT games with one. Now even I can look somewhat competent with one thanks to this game.
Since recent update, whenever I tried, I have always managed to get a time uploaded in the top 10 in EU with likes of R33, R34, M4 Gr.4 and 911 RSR cars with enough potential to get top ranking position if I could string my best sectors together. It is also quite easy to get up to speed, even if I'm quite rusty, it doesn't take long to be reasonably competitive. I wonder how well some top pad drivers of old would do but most seem to have transitioned to wheel by now or gone missing. Maybe some of the top pad and wheel users will make a return once official championships begin.
Anyway, below is last TT I did on GT Sport. I narrowly missed out on first on this, probably was so close due to no one doing a top drawer time in EU. 1:57's would have been more of a decent time which is what I was aiming for, messed up a few goes quite badly through 130R, even this one I was up on first but lost the little time through there which cost me top spot.

Maybe just bad timing on my part on DS4 but I reckon it is an area where wheel might be easier to nail such a corner thanks to more ability to adjust line mid-corner better. Overall I lost little bit here and there in sectors 1, 2, 4 and lost a bit more in sector 3. Looking at the replay, impressed how good GT looks and sounds nowadays but also shows how well the DS4 steering algorithm is that it can look quite close to wheel driving. I'm not doing it full justice, need some of the pad aliens to show how it is really done.