The CAR does have more damage up close than the Carbine at close range, but it's still the same number of shots to kill. CAR being as good as or better than Carbine at long range is ridiculous. It doesn't depend on "what you're used to." The R101C has lower recoil and more damage at long distance. If you're successful at range by burst firing the CAR you will be more successful at range by bursting the Carbine. The reason the CAR is good in the first place is that it performs better in close quarters than the Carbine. If the R97 surpasses the CAR as a close range option, alongside the Shotgun getting a range nerf, then it steals a significant portion of the CAR's appeal.
If you're skilled enough to consistently outgun Carbine users with a CAR at extreme range you can probably handle the same thing with the R97. I feel like a lot more close range battles are decided by 1-2 bullets than long range battles.
Hey, I'm basing this off of experience. I have had to switch to Carbine from CAR many times to reach Gen 10, and I have even played on PC on another person's account and the difference is night and day. The Carbine doesn't have the same sort of recoil as the CAR, and it is not better.
It actually sounds like you don't use the CAR over the Carbine, but if not, give it a proper try.
In Titanfall, where you hit your opponent matters. Legs, head, chest etc. It isn't as simple as 5 or 6 hits. At extreme long Range the CAR and Carbine are practically equal, but from close, mid, and mid-long the CAR does perform better.
I have also used the R97 a bunch, and it is weak close and extremely weak at long range, to the point that it is never worth trying. I have to also state that no matter what, a weapon that is atrocious at mid-long range (whatever distance you are imagining) it isn't worth using. The R97 can kill in half the time as the CAR at close range, and it still won't be the better weapon over all with that awful range.
I am even struggling to see how the R97 could perform better than the Carbine. To put this in perspective, I find the Autopistol and R97 to be basically the same except one doesn't really have any ADS worth mentioning and slightly less ammo per clip, but other than that they both currently feel the same.