It's a difficult one for me. I guess most UK based people will probably prefer the FA Cup but winning the Europa League, and especially the UEFA Cup back in the days, gets a lot more recognition across Europe. We knocked out better teams to get to the final as well (not saying you had an easy road but West Ham are not Dortmund level). Personally, I'd still rather win the EL but the FA Cup comes close. League Cup is miles behind though, completely irrelevant compared to those two imo.
And like you said, the additional CL qualification makes it a huge deal. It'd be gutted if we lost just the final but to lose the final and CL qualification would be devastating, also regarding possible transfer targets in the summer. Big, big game for us.