The compelling feature is that when QC 9 comes out, there is supposed to be no more TD. Other than that, QC which is really TD, is more stable, easier to use, (I think), and looks more like a real program than a test tool to the uninitiated. Plus it runs on Linux! Anything that runs on Linux has got to be good.
Quality Center is the TestDirector port to a J2EE platform (more stable than before). It allows for easier replication (via itself and SQL Server & Oracle) of data and multi-site usage (better utilizes IIS (especially IIS6) and Apache). It does incorporate the BPT functionality as well as a couple of other nice enhancements. It also opens up the 'Dashboard' functionality.
TestDirector was predominately based on ASP and had maintainability and performance issues (replication and mult-site usage). Also, with QC you get rid of the MS-Access code in favor of MSDE/SQL-Server for initial setups (this was implemented in QC 8.2 Standard Edition). The first version of QC 8.0 only supported SQL-Server and Oracle (no Access).
So what all does this give you? Flexibility and Maintainability, otherwise the functionality is relatively the same. Mercury is trying to move its technology forward.
You are correct, it does host a BPT process. Some companies have embraced BPT to a grand scale, but I have yet to hear of a really impressive success story. To me, BPT is Keyword technology and we have been using that for 6 years. With keyword the goal is to have manual testers actually write the automated tests as they build their manual tests. The case with BPT is to have the BA's construct their business tests with it. Although QC & QTP have a lot of pre-scripted components for your use, someone still has to script QTP to handle many of the processes involved with testing at such a high level. Don't be sold on BPT with the idea of no-scripting, which is similar to the sales hype about Capture/Replay of their functional test tools.