There are a bunch of ways of going about disassembling pallets that have their own benefits and drawbacks. If you just need the slats and aren't worried about pulling the nails from the stringers then punching the nails through the board usually helps avoid splitting the slat and it will come loose easily. I worked on a few different buildings where they didn't do the flashing on the roof correctly and we had to go in and tear the siding off to replace all of the OSB that got wet and moldy. We used an old nail gun and dry fired it into the nail heads to punch them through and once you got every nail the whole sheet would come right off. Not that I recommend ruining a good nail gun, but you could use an air chisel or palm nailer with a punch to push the nails through instead of fighting with a chisel attachment and risk splitting a lot of the slats.
A cats paw/bear claw tool is also really handy. I've spent many a day pulling nails out of boards using one. They will mar up the surface, but it will help avoid splitting the slats so you get more usable wood. They are particularly useful on nails that didn't go in straight and got bent over where other methods may not work as well. Mine is a larger Vaughan brand with a soft grip that works great for framing nails, but you might want something smaller.
For smaller projects I have propped them up a bit with the board I want to remove unsupported facing down, used a chunk of 2x4 and whacked it with a hammer, but that could get quite tiring if you are doing more than a few pallets. I've seen quite a few contraptions on YouTube where people make a long pry bar of sorts so you don't have to bend over and wear out your knees and back. Izzy Swan makes all sorts of amazing contraptions and of
course he has a DIY tool for this task that looks interesting and reuses the acme threaded rod from an old scissor jack: