Strictly speaking, the best Elite game is the
Archimedes version ('ArcElite'), at least if you're going by reputation alone. I'd have a more concrete opinion, but my attempts at post-Beeb Acorn emulation were abortive at best, so I never got to try out any of the alleged cool features. This, by the way, is the 'Atari ST' version Skyway is talking about.
The best version I have played would be
EliteA, a fan enhanced version of the original, BBC, version of the game. It has a fair amount of the stuff that made Frontier good, but with the original 'dogfighting' combat model. I know some people will try and tell you that Newtonian physics are better, but if you don't regard combat as a chore in Frontier, then there's a good chance you're autistic. Get that checked out.
Real men, of course, play the unadulterated Beeb version, As It Should Be Played. I still have the original manual.
In terms of remakes,
The New Kind is quite good. It's basically just a port of the original, but with colour graphics and various other things. Docking is no longer fuck hard though.
Here's a download link - bear in mind I haven't (and won't) look in the archive that gets downloaded, by the way.
Oolite is quite fun too. I gather it has a number of the features boasted by the Archimedes version, and is highly moddable. The main problem is the programmers are concentrating more on fancy graphics enhancements instead of OPTIMISING THE DAMN CODE. I find it a bit slow on my shit old PC considering what it is, you may have better luck.
Finally, here's the
best BBC emulator (may be a bit slow on very old computers) and a
site full of games for your perusal (including Elite and EliteA, of course). The Beeb also has the best versions of Exile, (Super) Defender, and Thrust, so look at those too.