I recently purchased a home that has a red quarry tile floor installed over concrete. It's the same kind of floor you would find in a commercial kitchen. I'm going to have new hardwood floors installed and need to decide whether to install them over the tile floor using a glue down method, or remove the tile and add a sub-floor which can then either take glue or nail down. The only obvious drawback I see to installing over the tile is losing the height in a room with only 8' ceilings. I could use some advise.

First I'd check a spot to see if its mud bed set. That means its set in a thick bed of mud and costs a ton more to remove than set over a thin bed. The tile and slab still needs to be flattened, ground flat to industry standards ie high corners and low spots filled. If filling low spots on the tile needs to be roughed up to make sure the patch sticks. Then you can still get MVE's through the tile joints so you'll need an excellent adhesive/vapor retarder.
It's not a DIY job thats for sure.