I know it might be irrelevent to consider this at so high bitrates but I would like to know if there can be a difference in quality (even theorical) between a mp3 encoded with lame 3.90.3 --api and another encoded with lame 3.96 or 3.97 --api?! are only vbr or low cbr improved in newer versions of lame?

I wouldn't say that, since alt preset insane is also used by many, it would be safe to assume that 320k continues to be improved on (even if it is overkill for most music)

Yes, there can be a difference in quality. In the LAME Changelog, there can be seen many features and bug fixes affecting quality which were introduced after 3.90 and affect all bitrates.

so, if i wanna use exclusively --api, which version shall i use? official HA one or latest?

I would say either or both. If you want to stick to the time-tested version, go with 3.90.3, but if you want to help the developers with the next stable version, you should use 3.96 at 320kbps, and report any quality problems here with the problem sample and your ABX results. Or you can try both and see which one you like better, and if you find obvious quality difference, there is a thread here that keeps a log of which version is better on which samples. You can add to it.