Replying to Looking for some input on my first tele lens

Hey dudes! it's one of these threads again. I'm looking to pick up my first high quality tele lens, I've been considering three and I wanted to hear some input from what you guys are shooting with.

Ill be using it on a GH4 with a speedbooster XL, I mainly plan on using the lens in the back country.

The three I have been considering are:
Canon 70-200 f/2.8L IS
Canon 70-200 f/4L IS
Canon 70-300 f/4-5.6L IS
Tamron 70-200 f/2.8

My main concerns is whether or not I can get away with using the f/4 or 4-5.6 on a crop body in lower light situations. I'd love to be able to save a bit of cash from the 2.8, plus the f/4 will end up sharper. I'm up in BC so as many of you know conditions get cloudy QUITE often.

For the Tamron my worry is durability since it is a plastic bodied lens, I'd like for whatever I get to be able to take a bit of a beating as well as a bit of wetness.

Cheers dudes!