My personal head-canon for Doctor Who (for which I claim no actual _evidence_) is that regeneration involved the Time Lord essentially 'restoring' his body from 'back-up' but where that 'back-up' is alternate possiblity of their life that never came to be. So it's possible that they will look very similar but the odds are against it. Also the post-regeneration issues are usually because a section of the Time Lord's mind is straightening out the real memories from those of the alternate timeline that only exists in the new body's mind.

Of course, I also treat the 12 regenerations as more the 'Gallifrey Book of Records' number than as a hard limit. It's not as if Time Lords go out of their way to surpass it but if you're dying _anyway_ then you may as well try.