I prefer the TTO since they are simpler to use, BUT, I am selecting a razor more based on how it shaves, rather than on how easy it is to use. My current favorite razors are the 37C (3-piece), the EJ89 (3-piece), and the '67 Aristocrat (TTO).
I like the 3 piece razors. I find them easier to manoeuvre under my nose. Also, I find them easier to clean than TTOs (not that TTOs are especially difficult to clean!)
Three-piece. Simple, compact, easy to clean, easy to shave around my beard, fairly bullet-proof.
TTOs are nice, but they are harder to clean, they make shaving around my beard more difficult (because they are relatively bulky), they don't compact nearly as well as a three-piece (say, for travel), and there is always something that can go wrong...
TTO Superspeeds seem to work better for me, they have a very natural angle in my hand.
I'm not opposed to 3-piece razors, they're just not as effective for me.