Let’s compare the two, side-by-side.
First up, we have Star Wars’ hyper engines that go through hyperspace compared to Star Trek’s warp drives that travel through normal space at FTL (“faster than light”) speeds. Technical data books indicate that the speeds and range of hyper drives are greater, however.
We have also repulsor craft that hover over the ground in the Empire, but not much is shown of Federation ground transport, although anti-grav units are used to move heavy objects. But the Federation has one edge: teleportation.
I’m going to consider them even here, based on having different advantages.
Both empires seem to be able to produce unlimited power for their needs. The amount directed to any one use might be limited, but fuel seems to be endless. While the exact fuel for the Empire is unclear, it seems to be on-par with the Federation’s antimatter engines (although often at much larger scales, e.g. The Death Star).
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