Here's my take:
Roatán wins for gorgeous beaches and easy access to snorkeling from shore. The nicest beaches on Utila are reachable by boat from the main town area, so unless you're planning to rent a place reachable by boat or take day trips to them, you'll miss out on that. We've found good shore snorkeling on Utila, but it's much more difficult to walk to than what we've experienced on Roatán.

There are 2 ferries/day to each of the islands but far more flights to Roatán than Utila. Not hard to get around either once you're there. Roatán is much bigger and more mountainous which means there's more to do in addition to the water stuff including some wonderful hiking in the Carambola Reserve and some interesting, diverse towns.

The dive sites are, in general, closer on Roatán than on Utila, where you'll spend more time on a boat since many of the best dive sites are on the north side of the island. You'll be really, really, lucky to see whale sharks on your surface intervals from either place but Utila definitely gets the nod there - they're extremely rare on Roatán.

In general we've found Roatán more spendy than Utila but we've loved the food both places. On Roatán we've preferred off the beaten track places in Sandy Bay, French Harbor, and Camp Bay than the more popular West End and West Bay options. If you want night life and a selection of restaurants, though, pick one of those. On Utila here's the place we love, on the edge of town near the bridge leading to the old airport:
http://www.aboututila.com/AccomInfo/LightHouse-Hotel/Index.htm

Wow, thanks!!!

Oh wait, could you please tell me what means of transportation are most commonly used to get around Roatan? Car? Bike? Golf Cart? Is it necessary to have motor transport every day?

Depends on where you stay and what you want to do. Most folks stay in West Bay or West End and just use taxis or water taxis as needed. To get to the east end of the island you'd need a rental car (or motorcycle?) or driver.