According to these benchmarks, the SGSII blows the Nexus, and other handsets, out of the water... even though it's running Gingerbread.... on half the benchmarks.
The article goes on to say, that ICS will improve the SGSII's performance by 30-40% which means that it is the clear winner.
Samsung Galaxy Nexus benchmarked, shows much improved browser performance in Ice Cream Sandwich
Added to this is the news that the Ice Cream Sandwich code is to be released soon and things are looking even better for the SGSII.
Ice Cream Sandwich Source Code Will Be Released Soon