I've installed and used ALM Synchroniser before. Best that you prototype it on a sample project first to make sure it can synchronise the fields that you need (Jira for example uses tags, which don't sync) and make sure you test for volume - we found it very slow over a couple of hundred records.
Task Top don't provide a demo for you to try, but they will offer webinars or on-site demos of functionality. They'll also insist on installing it themselves, so cost may be a factor here.