Here's how you would do this. Forget minimization, you don't need it. Take NFAs (or DFAs, it doesn't matter) representing all the regexes you want to compare. Mark the final state(s) of each NFA or DFA with something that identifies that particular regex. Then combine them all into a single NFA using alternation. Finally, convert that NFA into a DFA, but when you do, make sure that each final state of the DFA has markers indicating what regex(ex) it was final for.

Now survey all your final states. If all final states have markers for all the regexes, the regexes are equal. You can also use this to determine if one is a subset of another (all final states have markers for regex1, but only some have markers for regex2), if they overlap (at least one final state had markers for both regexes), or if they are completely disjoint (no final state had markers for both).