There isn't much of a difference.
Acoording to OGP Stats in their 1998 report singles have the lowest accident rate per 100,000 flight hours, followed by heavy twins.
According to HAI stats over the past 10 years twins have slightly lower fatal accident rate than singles. (.83 per 100k for singles vs .72 per 100k for twins)
(It shows singles have a significantly higher non-fatal accident rate 4.45 per 100k vs 2.67 per 100k for twins) Much of the difference is successful autorotations.
http://rotor.org/portals/1/safety/2005/4.pdf
have to do your own math to get 10 year numbers.
It is noteworthy to add that these are US helicopter fleetwide, not just oil and gas, so your single engine stats include ag, powerline, animal capture and other higher risk flight profiles.
As SASless said different environment. shorter flights, calmer water, as well as the often touted different government, customer thing.
I fly singles, (not in the gulf) and would feel no safer in a twin. I would however, feel less safe on any type that has only a million hours under its belt. Greatest new technology or not, there is value in 30 years of refinement, and an element of uncertainty in anything new.
Look at the EC 225 the S-92 the AW 139 and the EC 135, all NEW aircraft certified unther the new, more stringent regs and the source of many of the worst accidents in the past few years. All growing pains I'm sure. And I have no doubt at some point they will be safer than the models they replaced, but we wont know that point until we've passed it, and I'm not sure we have on some of them.
I agree with what the other guy said about the second pilot, I think that helps a lot more than a second engine.