I think a lot of people still associate OpenVZ with Plesk/Virtuozzo. I must admit I haven't seen where that stuff has been going, but 6 years ago it was all pretty horrible.
There is, at the core of OpenVZ, something that seems absolutely elegant and useful – a more isolating take on the FreeBSD jail concept, which itself was of course chroot on acid. Using it for advanced process isolation looks like a sensible application. The _typical_ application of OpenVZ, in the field right now, though, is that of a poor man's hypervisor. I think that a container technology is just the wrong approach for this.
The big elephant in the room, for me, is security isolation. Containers all run under the same kernel, which means that a kernel compromise is a compromise of all attached security domains. An actual hypervisor setup adds an extra privilege layer that has to be separately broken.
Again, this doesn't mean that OpenVZ cannot be tremendously useful. The most visible way Parallels is selling the technology, however, is not what people are looking for. This pans out in the market place.