I've been using emacs for quite a while.
Flymake is one of the features I really appreciate about emacs, and yet I wish it worked better. It's hard to configure and it can be a resource hog without fixups.
I had to hack around with it - to get python, php, java, css and JavaScript and various other languages working. Also had to add flymake-cursor to get the errors to appear in the echo area. And another patch to convince flymake to run only on visible buffers. But this jalopy pretty much works now, and I don't worry too much about it, except when I pick up a new language. (Adding flymake for Go today.... is how I became aware of flycheck)
Flycheck is "supposed to be" better, according to this article.
Do I want to invest the time to switch?
(I don't really care that flycheck will never be part of Emacs)
I don't have relevant experience, but I will note that fixing what isn't broken is never a necessity, so why not keep your existing working configuration for flymake, but try out flycheck for new use-cases?
If you like it, keep using it in new situations; and if you find yourself needing to modify any of your flymake configs, you could consider migrating them to flycheck at that point.
If you really like it after that, you might feel inspired to migrate everything (which will probably be easier with a bit of experience under your belt).