I know about versionone and rallysoftware, I don't know about axosoft. I can't say which one is better because to be honest we didn't stick with any of them. I do remember we also used Atlassian's Green Hopper which wasn't bad, but I wouldn't vouch for it either.
I think you have to try and test them yourselves. It would be nice though to update this thread with your experience with each one of these tools based on the following criteria:
- Features
- Stability
- Interface
- Ease of use
- Support