I've got a lot of both of them.
When you go to the low end of both brands it's Vanguard all the way. The cheapest SPS type stocks are junk where the Vanguards are at least somewhat better. SPSs tend to have bolts rough enough to use as a file. Some makers of $2000 rifles could learn a bit about feeding by looking at a cheap Vanguard.
Once you go up the ladder in price you can go with whatever grabs your fancy. You could just pick the stock you like and let it go at that.
Remington's design is full of cost cutting short-cuts that haven't really caused much problem. Things like the bolt body being made in three pieces and soldered together; and the washer style recoil lug. The Vanguard bolt is forged in one piece; and the action with integral lug is either forged or extruded depending on who you ask. The Vanguard's extractor is the M-16 type and although it probably won't pull cases out any better it is slightly superior in that it won't render the whole rifle inoperable with a few grains of sand stuck behind it like a Remington can be. The no tools field strippable bolt is a nice touch. You can do the same with a dime and your bootlace on a Remington if you know how.
Both are likely to shoot very well out of the box. The Vanguard is warranted to shoot, for whatever that's worth to you.
If you are planning on building on the action later, you probably should go with the Remington. Its not so much because the action is better as that the aftermarket is shaped toward it and every gunsmith and his brother knows how to work on one.
Out of the box triggers are better on the Vanguard. It never used to be that way. Vanguard bottom metal is a little chintzy. Remington's is a little less cheezy and there are quality replacements available.