I regularly run V8 and Sunspider benchmarks on both Rhino and Spidermonkey (disclaimer: I'm a committer on the Rhino project). The current Rhino release (1.7R3) is still quite a bit slower than Spidermonkey, but recent git snapshots have caught up nicely. (Note that I'm talking about interpreted Spidermonkey without Jaegermonkey or other JITs - Jaegermonkey is way faster.)
On V8-benchmarks-v5 Rhino 1.7R3 scores around 360 on my machine, Rhino git master 480, Rhino git rhino_1_8 branch 570, and a recent Spidermonkey build around 540 (higher is better).
For Sunspider 0.9.1, the numbers are 8890 ms for Rhino 1.7R3, 2250 ms for Rhino master, 2180 ms for rhino_1_8 branch, and 1390 ms for Spidermonkey (this is milliseconds so lower is better).
All Rhino benchmarks are on Oracle JDK 1.7.0 with the server VM and default settings and after a few rounds of warmup. With recent Rhino snapshots you can easily run the benchmarks yourself using the ant benchmark-* targets. My Spidermonkey build is a few months old snapshot built with standard instructions.