you're spoilt for choice on the road bike front, so that would be the obvious choice.
However I'd take the mountain bike, theres lots of great mountain biking around there, its just that its a less well trodden (ridden?) path.
Head into soller (town not port) and find tramontana tours, buy their biking map and explore, or pay for some guiding from them.
Me and a few friends took our mountain bikes out there 3 years ago, we found various gps tracks on the internet, they were pretty decent.
A memorable one was the pilgrims steps (just google it), start at cuber reservoir at 800m altitude, and descend down hundreds (thousands maybe) of steps back into soller town.
Also the GR221 path is decent I hear.