BAs in my company use Word, Excel and Visio for requirements definition reasonably well.
What are the key advantages and disadvantages of using a requirements tool instead?
I've found that you don't, to put it simply.
A requirements tool is a bit like a bug tracker for specification documents, instead of a spreadsheet of points, you'd store the excel rows in the tool instead. So far, you might as well use a big tracker for this!
Requirements tools then add a lot of complexity to the system, references between requirements are added that are supposed to help, but unless you only have a few, you quickly get into a mess. If you have a list of requirements in Excel then you're already managing requirements well, so the reference features of a req tracker is an unnecessary distraction for you.
What these things do for you that is useful is to allow modification and traceability of the implemented requirement through the software development/delivery cycle. So when software is written code checkins are associated with the requirement, when it is tested, it gets associated with the requirement, when software is built the list of requirements in that software is listed, etc. Obviously this means your workflow has to be much more rigorously controlled - you cannot do anything outside the process, or the whole point of using the tool is invalidated.
There are lighter-weight requirements trackers like Polarion, these are much better than the complicated old tools like doors which I would avoid like the plague - unless you have very expert analysts used to using such things.
The biggest disadvantage of a requirements tracker is that it stops your BAs from working with the requirements and makes them work with the tool instead. When we tried it, we went from a 2-man BA team to needing 10, the tool slowed things down so much we junked it. (mind you, this was an "enterprise" tool that was 100% pants).
Requirement Management means mostly
For easy tasks you can use MS Office, but if you have more than a single specification and if documents tend to be larger than 10 pages, you should use a dedicated tool. no single question I noted above can be solved by using MS Office, also Office Documents are not searchable, you cannot refer to parts of other documents easily, no version control(baselining) and working in a team on a single document is more or less impossible.