Is it worth submitting papers to "graduate" peer-reviewed journals?
You want to publish papers in the best journal or conference you can. If your Masters thesis can be published in a serious journal, you should attempt to send it there. Publications are the currency of academia and a publication in a better journal often translates to higher value.

However, there are lots of reasons to send it to a "graduate" or lower-tier journal. 


The journals in your field might consider a thesis to be previously published and they might not accept previously published work.
Your Masters work might be unrelated to your PhD work and you'd rather spend your time working on new more important work.
Your thesis would require a lot of work that would take away your new work. It might be better in the long run to work on new ideas as opposed to spending time trying to clean up or improve your previous work.


Without knowing your exact situation, it's hard for random strangers on the Internet to make an exact call. You should talk to your adviser or a professor in your department to get more informed and personalized advice.

EDIT: I should point out that my experience have all been in computer science. Things may differ in the social sciences.