Barry uses the Bond theme full blast in many of his scores, especially with Moore and Dalton. It comes up twice in MR, OP (probably done to make it seem like a real Bond compared to NSNA) and TLD. It's there once each in TMWTGG and AVTAK, I believe. FRWL has James Bond with Bongos, which is almost the Bond theme. YOLT and OHMSS use Barry's original arrangement of the theme for DN, but perhaps that's more the editor and not Barry's choice. I don't recall the theme full blast in GF, TB (unless you count the end) or DAF, but Barry makes some very good use of the Bond theme.
Suits - I'm not suggesting that Barry doesn't use it. I guess to clarify, there's using the Bond theme, and then there's falling back on the theme and it's the latter which I felt Arnold relied on too much, especially in, and to the detriment of, his earlier scores.
It's interesting when talking Arnold, how often people are very positive about CR and QoS. I know I am - I think they're his best, and very good by non-Bond standards. In both, the decision was made to heavily restrict the use of the Bond theme. As a result, Arnold overall, was much better IMHO, across the rest of the score.
I'm not one of those people who thinks the theme should be axed or anything! But for Arnold specifically, it seemed all to easy just to go to it. To defend Arnold (who I don't think was bad by any stretch), in both TND and DAD he was denied the title song to build the rest of his score around, something which Barry (and Hamlisch especially) did very well. So to be fair, without that riff, you're either using something else which isn't familiar (his use of Surrender in TND is most-Barryesque, but unfortunately thanks to people above him, we don't hear that until the end of the film), or going back to the Bond theme. Which he did. Often.
Unfortunately for all potential scorers out there, when you sign up for Bond you are signing on to be measured against Barry, who was the first, the trendsetter, the genius (and not just with Bond). So Arnold, Newman, Conti (alright, not Conti) all come in for stick that probably isn't quite reflective of their efforts. Hamlisch is the only one who really elbowed out some space on that top line.