Our forestry equipment is divided among the pumpers primarily, plus some is just stored at the station.
All told, we typically arrive at a brush fire with 1500' of 1" forestry hose in backpacks (300'/pack); a dozen rakes, a dozen brooms, and a dozen collapsible Indian Tanks (backpack pumps). I don't think I'll ever see them all used at once though
The forestry hose is really only used when the fire is out of reach of standard structural 1.5"/1.75" lines, and needs extensive overhaul.
A typical crew is two Indian Tanks, two Rakes, and two Brooms. The first indian tank knocks down the fire; the second works on hotspots on the fire line; the rakes are a cutting tool, and cuts small brush and drags them into the fireline; the brooms follow and sweep the leaves and debris away to create a dirt path around the fire.
If close to the road (most of the time) a hose and some Class A foam takes a lot of the work out of it.
We don't have to use chainsaws often, so someone would run home or get one off the ladder -- I do remember taking a small dead tree down once with an ax though
We do have a 80gpm/200gallon tank CAFS system on a Hummer chassis -- Hummer will go anywhere, but it's certainly wider than a pickup with a slide-in unit, and maybe wider than a pickup with a custom fire body on the back. It doesn't carry any forestry tools -- when it's going in, we grab tools from the pumpers and walk in with them.
Major fires far off road, we'll usually call mutual aid for another Service or Forestry truck to assist us, and they usually have a portable pump with them to help, too.