I don't have any experience cycling through large multi-lane roundabouts, but the small ones I find easier than normal intersections. I can negotiate them at higher speed on the bicycle than most motorists seem able or willing to go, and I can choose what kind of gap I like before entering. I haven't had anybody fail to yield and enter a roundabout too close to me while riding in one - yet - but the slow speeds involved make it seem like it would be easy to take evasive action.
As I've become more confident I've found myself entering small roundabouts more readily, accepting somewhat smaller gaps before approaching cars already in the roundabout since they won't need to slow for me given my ability to match their speed. A redneck in a pickup truck entered a small roundabout at high speed from a street ~90 degrees to my left at the same time I entered it from my street. He seemed intent on intimidating me, but he overestimated his cornering ability, and squealed his tires around the curve and slowed down before reaching his exit, well after I had passed it.
As roundabouts scale up, their speeds increase, and I think the safety benefits for cyclists decline. I ride regularly through free-flowing slip-lane type intersections, and it requires a lot of attention, despite having only one or two conflicts to deal with at a time. Multi-lane roundabouts have a lot more going on at once. Hopefully drivers will learn to put down their cell phones when approaching roundabouts of any size, and pay as much attention as I am.