So I've got some grill strobe lights for my pickup truck, and I plan on wiring them up the first day I don't have to work. I was wondering what, if any, are the pros and cons of ground side switching and power side switching?

Power side for sure. The ground side shouldn't need to be run all the way to the battery anyways, so it only makes sense to switch it on the power side. I would try to throw a fuse in the circuit if its possible as well. Just in case the insulation on your power wire gets rubbed off or something. You never know what could happen.

OK, but a quick question. How many amps should the fuse be? I have head light and tail light strobes in my truck as well and the fuse says 250v and it's a 60 watt strobe kit. I only run 2 strobes instead of four because they're brighter the less I use. The capacitors on the grill strobes say 350v so I figure they're higher wattage than 60 watts. Plus there are only 2 lights on the grill strobes.

This, I've always found it personally preferable to run power side.

What you need to be concerned about with a fuse is current. Voltage is irrelevant. If the strobes are 60W then the fuse should be at least 5A. When the alternator is running the voltage will be higher than 12V so a 10A fuse should be suitable.

Power side or ground side doesn't matter most of the time. I'm very sure there is a list of do's and don'ts about which side to use when dealing with electrochemistry of diffeering metals, but it's not a big deal for DIY projects.