Are there any known differences between the Mediakite and Sourcenext versions? RE2 and 3, for example, seem to have considerable differences between their Sourcenext and Mediakite ports. I was wondering if that was the case with Dino Crisis.

Mediakite is essentially / based on sourcenext but just modified to be more friendly on modern hardware. As far as i know there is no mediakite port / version of the game and the sourcenext version is nothing else than the JP PC version re-packed to be more friendly on modern hardware (well modern back in WinXP times). Additionally pc version comes with arranged mode which equals to consoles Hardmode (similar just as with the Resident Evil games)

If it comes to which version is the fastest, its actually close fight between the PSX Version and PC version (run nativly) if run via emulator you get slower results! However as Dino is fairly unpopular to Run i havent spend the time yet to figure out why / where you get that significant time save between versions besides lucky RNG