A top mount sink WILL result in water damage as water will puddle around the rim.

I think making sure you wipe up water when finished, is a good idea. Either sink can result in damage. Its how you treat the wood that matters too. Mineral oil, I feel is the best. I have a butcher block island and I use it, we sit glasses of ice cold drinks on it and my colander drips water all over after rinsing veggies and we've had no problems with stains or water. But I believe a natural finish is the key. When you have a hard finish, it can scratch and wear, that's where the problem begins. Water gets trapped under the finish and cannot dry properly, and causes mold and such. That's my experience. Good luck! Do a Google image search, you'll see pros and cons.