I don't know if there's a West Coast / East Coast "thing" in firefighting or not, but there is definitely a marked difference from very urban departments (FDNY) to very rural departments (my department in rural NC).
For one, we had little or no reason to training in high-rise firefighting tactics. We had no buildings more than 2 stories in our district and those were residential, with no standpipes or any of that stuff.
OTOH, I guess most FDNY companies don't respond to a lot of brush fires, or have to deal with a lot of urban/wildland interface stuff. I'm sure there are some, depending on the exact location, but how much wildland / brush is there in downtown Manhattan? For us, brush fires, including very large brush fires (think thousands or tens of thousands of acres) were something we dealt with semi-regularly.
There are differences in equipment as well. FDNY can usually rely on hydrants, whereas we had to do a lot of stuff with running tanker shuttles and drafting from dump tanks, drafting from static water sources (ponds, etc.). And even when we had hydrants they would probably be further away due to the difference in spacing (ours were every 1,000 feet where they exist, most major cities have a "hydrant on every corner" or "hydrant ever 500 feet" or something policy), which mean longer hose lays, more relay pumping, etc.
I've sort of always seen the urban/rural difference as one of the main "branches" in the fire service (aside from paid vs volunteer).