At the risk of being labeled the poster boy of budget builds here is how I see it:
Custom actions are a must for any cartridge larger than RUMs. Yes you can get 338 LM built on one, but smiths kind of frown on it. Custom actions will be built to spec and will work right out of the box. They can also have nice features (eg. side mounted bolt release, one piece bolts, fluted bolts, etc. ) Without question they will be stiffer and offer more threading area to provide better barrel support. And finally you will have lots better resale. If money is not a restriction, and you worry about resale ( I personally believe in "feed em barrels"), then custom actions are really the way to go.
If cost is your decision maker, and you don't care about resale, you can actually save lots of money by going the donor gun route. Watch the big box stores and the internet(Bass Pro, Dicks, Academy, Buds). They are always putting SPS 700s for sale for around $500.00. If you are going to go the magnum route, you need a magnum bolt face buy a 7mm Rem, easier to sell the new takeoff barrel. Look at the barrel makers that offer smithing services this is the best bang for your buck as an example hart will true your action, fit and chamber the barrel for $650.00 barrel and shipping included, if you subtract the cost of the barrel that comes to $300 total smiting costs. You can sell the barrel for about $60 dollars So now you have $1080.00 in a barreled action, trigger, and bottom metal. This is a good way for some people to get into the sport, that might not otherwise be able to.
Now after saying all of that, my next build will be on a custom action because while they do have nice features, they make a build look really cool