I'd say Washington. That wordmark logo is absolutely fucking horrendous. Give me either the screaming eagle unis from Ovi's rookie year, or even bring back the Weagle, but with the colour scheme from the 2005-06 sweaters.
I'm a Capitals fan and I completely agree. They switched to the current look the same season I became a fan, although it's been all I've known I think it's the worst logo in the league by some distance.
Nashville. Keep the colors, but trash that awful sabertooth.
I find that most teams that have cats as logos are awful. Panthers (both hockey and American handegg), Lions etc.
There has to be a cool visual idea for a predator that also ties to the paleontology-theme that they are going for due to Nashville having so many fossils.