Metropia is different in HD and Pulse because Metropia White is actually Metropia Reverse in HD. The jump was smoothened out most likely because it would otherwise send you flying too high in Phantom with the combination of two BRs possible (It already hits the roof of the ECS cage in Pulse). Then it was reversed.
Because of that, Metropia Black or Metropia Forward in HD plays better in HD than in Pulse.

The others do not require any such modification because you are not sent flying to high. The only slightly problematic one would be de Konstruct Black, the "shortcut", as you can hit the building when jumping on. However, this can be adjusted with pitch control easily, something not quite as easy on the jump in Metropia Black on Pulse when you're going for the two BRs.

So, yes, and not no