We're tearing out old carpet and putting down hardwood floors on a slab foundation. Are there pros and cons to gluing down vs floating the floor? And what about those trip-hazard transition strips? The new floors will abut existing tile floors in the kitchen.

check this out

http://www.bcfca.com/blog/floating-or-glue-down-hardwood-floor

I like the floating floors due to ease of installation and it's not near as messy as the glue down floors.  You will have a transition strip with either type of floor.  With the floating floor, you can float over a small hump in the concrete a little easier than with glue down flooring.  Another option is LVT (Luxury Vinyl Tile I believe).  Glue down/ peel and stick.  If a piece is torn or ripped, you can remove with a heat gun and replace one piece.  I've not personally used the LVT yet but have heard lots of good things about it.  Is this for a rental, flip, or personal home?  Those are also considerations I think about when choosing materials.  Also price range of home and value-add.  Hope this helps.  

Advantages to floating floor is doing repairs is fairly simple. You can easily split the wood open and replace the damaged boards. With glue down its not as easy to do repairs.