What are good reasons to jump from the PM to the Manager seat?
The most important reason: if you believe you'd like people manager job better than PM job go for it. It is said that when we find the job we love we don't need to work anymore and there's much truth in it.
Other reasons to transit from PM to people manager:
If working with people is something you like most about PM
If you want to try something a bit different for whatever reason, e.g. have richer resume
If you want to learn another perspective of the project - team manager has a pretty different one than PM
Often managers are paid better than PMs although the difference isn't that significant, however if this is your only motivation don't do it
I'd say that management position gives you better options in terms of advancing into top positions in the organization, like VP or C-level exec (see: Are Functional Managers or Project Managers Better Candidates for Executive-Level Positions?)
If all of the following apply, it may be time to make the jump:
- You are bored with managing the projects that you are being allocated;
- You understand the role of the manager, and are confident that you would be good at it;
- You want to remain with the same employer.
If not bored, don't jump, unless you need the money. Management roles get frustrating too, especially for someone who is as delivery-focused as most PMs.
If you don't understand the role, or have any doubts about your ability to be a manager, don't jump. Most management positions are, in my experience, pretty political, and that doesn't suit everyone.
If you have no commitment to stay, move on into a bigger, more interesting PM role elsewhere. I wouldn't recommend moving out of PM into management and changing employers at the same time, as you won't know what you are moving into.
Sadly, any negativity you may detect in my answer comes from bitter experience!