We also looked at TestLink in open source, and we looked at ALM. The functionality and the usage, and usability of TestRail is much better than any other product. It's not dependent on any ActiveX or any library. The client can use it out of the box, they just need to type in the URL and start using it. Also, the training videos are very nice. It covers everything, that would be all you have to do is just watch the videos for a few minutes and you can really just learn very quickly and easily. Other tools, like ALM, had issues with the training. 

I played a bit with DeskLink, but I've never really evaluated it.

TestLodge, Klaros-TestManagement, PractiTest, Test Collab.

No.

Yeah, Zephyr, Redmine, etc.

JIRA/Enterprise Tester: Felt less user-friendly and more complex to start with. Also, it was less adapted for coupling with a homemade automation testing tool.

I can’t answer this question because the choice was made before I came to this firm.