D7100 and a birding lens

Trying to keep this short and sweet. I'm pretty interested in either a 300mm f4 or the Nikon 200-500. I know I ultimately want the reach of the 200-500. It's at the top of my budget so a 500 mm pf isn't really in the cards at this point.

Presently I'm using a 55-300mm VR Nikon lens.

What is a reasonable expectation to have in terms of auto focus speed and sharpness improvement when comparing my current lens to a 300 f4 or the 200-500?

For anyone wondering, the 300f4 stays on the list because the reviews are outstanding. From my research I like the 200-500 over Tamron G2 and Sigma contemporary 150-600.

Maybe I should wait and just save up for the 500pf?