Well, there's one way in which the JS engine effects it: how efficiently one can call into C++ from JS. Mozilla have done a lot of work to reduce the cost of that in SpiderMonkey.
Sure, though in the grand scheme of things that penalty is pretty small when compared to the DOM operation itself. Eg. doing an appendChild() on an attached element and causing a reflow.
It depends a lot on what you're doing — if you're hitting fast-paths (esp. if you're dealing with out-of-tree nodes) it's entirely possible to end up with the JS/C++ trampoline being a significant part of the bottleneck, for much the same reasons as why Array.prototype.reduce can in several implementations.
