The question of how parallel Chromium is is too vague to answer :) There are a variety of limitations. Let me throw out some:
* If you share renderer processes, then one tab can block another tab if it monopolizes the main thread (or the IPC thread for that matter)
* I think you mentioned elsewhere you were using an extension. That extension could be the bottleneck for all your loading, if the webRequest API handlers aren't responding quickly enough.
* There are networking limits, like connections per host and what not.
Identifying all the various parallelization limits would be a PITA. In order to figure out what's blocking progress for you, I recommend using a debugger, about:tracing, and task manager (to see if any process is CPU bottlenecked), and perhaps about:net-internals if you think it's a networking issue.