I think it depends on your situation (doesn't it always?).
If you've got a lot of potential liabilities in your life (an old vehicle, old pets, sick parents who live far away, etc...), then I think an emergency fund needs to be a priority before accelerating your debt payoff.
If you've got few liabilities (no partners/kids, secure job, good health, etc...) then I think it's fine to get by with a minimal amount in your emergency fund and focus on paying off debt faster first.
I'm working my way out of almost $100k of debt, but I've been focused on building up my emergency fund for a while. I'm glad I did too - I lost my job right before Christmas, and I just had to take my cat in this week for an emergency $3,500 vet visit.
If I'd have focused on paying off debt rather than building up a savings cushion (even if it wasn't as large as I would have liked), I'd be totally screwed right now, potentially with a dead cat as well.