Buran was better
The Buran was better because
A. The launch system was usable for other things too
B. The craft was lighter once in orbit - needing less fuel to move around
C. It was fully remote capable
I'm not sure how one demonstrates A or B, it's just a fact.
No Buran didn't really have it's own engines like the Shuttle, they were just for orbital stuff - not for launch.
Perhaps you should ask NASA how they will maintain Hubble? From driving on the moon to not having a method doesn't seem like progress does it?
Why would the Soviets disprove Apollo? Easier to let the lie sit and take the grain shipments, it's coming back to bite NASA anyway.