A drop ceiling can be done so that you leave just enough room to move tiles if you ever need to access stuff, which would cost you about 2" in headroom. The downside is loss of headroom and the look, which some folks don't like.
Drywall can be done so that all you lose is the thickness of the drywall. The downside is the wiring issue you speak of, and possible leaks in your plumbing.
If the plumbing leaks, you'll be ripping the drywall down anyway, but you'll prolly have to replace ceilig tiles too, so I think that's a wash. The major difference is the repair work needed if you find you DO need to run more wire.
Cut BETWEEN the joists and cut out a chunk at either end of your wiring run. When you're done, you screw the chunk back up onto the ceiling (you WERE careful and not going Neanderthal, right?

) and mud the piece back into place. Not that hard, and if you put some effort into it to make it look nice, you'll never notice the area you cut out. Using a fish tape would make even less of a repair hassle, but it's been my experience that people can't figure out how to do that type of "arthroscopic surgery" and they're better off cutting the larger chunk.
Other options are making access panels into your ceiling on the off chance that you haven't run enough wire or need to get at your joist area to run wiring.
Unless you have 7' at joist level, I'd go with a drop ceiling. GO INVESTIGATE WHAT THE PANELS
CAN LOOK LIKE! Lots of times, people think drop ceilings ONLY come in that "been hit with buckshot" look and simply assume that's what they all look like. You can get many different patterns - most folks just don't like to do much special ordering.