The only aftermarket difference between Remington and Savage are you can buy a better aftermarket trigger for the Remy 700 than what is offered for a Savage 10/110. Jewel is probably the best aftermarket trigger made.
But there are several very good Savage triggers out there.
Stocks? What ever you want for either brand is available in general. If you have an older Savage SA staggered feed style action,you are limited on stocks now since most stock makers only stock the newer center feed style stocks.But,Manners,McMillan,and a few others still make them for staggered feed actions.
Savage LA makes no difference,the spacing for the action screws is the same. I used a 110 Center feed stock on my 110 Staggered feed 6.5-06 build. I just had to open up the mag well of the stock up 1/4" to clear the blind magazine box.
If you want a DBM for it,there are several choices,and PTG even makes bottom metal kits for the older Savage staggered feed actions.
Barrels? If you're wanting a top end barrel like a Hart,Pac-Nor,Bartlein,etc..They don't offer any Pre-fit barrels for a Savage,so it cost the same as a Remington 700.
E.R.Shaw,McGowen,Shilen and a few others offer the Savage Pre-fits,and they do save you money doing it yourself. And in my experience,they will hold their own against most barrels for accuracy when you handload ammo for them.
Criterion barrels makes a RemAge barrel for the Remington,and it uses a barrel nut just like a Savage.But they have a limited number of chamberings that they offer it in.
Either action will work well for a custom build,and IMO,neither brand has any advantage.