Greeting SIGguy229; and others,
While the two blades you mentioned are probably adequate for most of your intended purposes, the prying task may not me all that well received by either the RAT-5 or the Gerber LMF. As far as cutting tools, and even for light batoning (swood splitting), both will most likely perform well.
If you would be willing to consider a slightly larger tool, may I throw out a suggestion - take a look at Becker Tac Tool, now being made by Ka-Bar: https://www.kabar.com/product/productDetail.do?productNumber=BK3&mode=category&categoryId=1,2,3,7,8,9&categoryName=Military/Tactical
I got my first Becker Knife & Tool Tac Tool in 2000, and it served as my #1 go-to camping blade for a good 6 years. It will carve, pry, chisel (wood), chop, and take a baton all day long. It is as heavy duty as an edged tool can get.
One of my Tac Tools with a ‘fancy’ baton I fashioned while splitting wood with the Tac Tool:

The Tac Tool is chisel-ground. Some may say this an issue when carving, but I’ve never had a problem. Maybe it’s because the grind tends to favor the right-handed user, or maybe I just haven’t tried to make intricate carvings when camping:

If you prefer to have something a little shorter, and would rather have a more traditional blade shape, consider the Becker Companion. It, too, is a sturdy package! https://www.kabar.com/product/productDetail.do?productNumber=BK2&mode=category&categoryId=1,2,3,7,8,9&categoryName=Military/Tactical
Again, those are mere suggestions. There are lots of knives out there that will fit your needs (except for the prying part). Ultimately, I’ll recommend getting something that you like. Good luck with your search.