Stubbs,
Been a gun and hunting nut since I was 8 and I'm 50 now. I have gone the route from high velocity back to standard cartridges and back again...maybe three times. We all have our personal likes and dislikes.
For what you describe either the Rem or the Win 70 is a great rifle to use as a start point. An 06 is a great do it all cartridge for north America. Then again so is the .270 Win and .280 Rem as well.
In my experience....Rem 700's; currently crappy triggers that need to be replaced or a competant Smith readjust. Generally VERY accurate right out of the box. Round receiver bottom that is easily bedded and is generaly bedded OK from the factory. An absolute plethora of aftermarket stocks and triggers available. RARELY feeding or extraction problems. STRONG actions. Decent stock designs. And generally discounted heavily. Tons of used Leupold/Refield scopes and bases available at gun shows...Cheap.
Winchester M-70, current controlled round feed style (CRF)...... The new LT models have a near perfect stock design from David Miller a premier stock maker, very comfortable and manage recoil VERY well. Flat bottomed receiver than generally should be rebedded for best results,though that is cheap. Probably the best and most easily adjusted triggers. Unchanged for many years, very reliable. CRF is anice feature, debatable if its needed but nice nne the less. Picks the round up from the mag, and holds it until its in the chamber, plus a tremendous amount of extraction area on the bolt.
Either / Or !! I suggest mounting and carrying each model in a store or shoot at a range if possible. See which one feels best.
Scopes and mounts.....TWO piece bases,e asier to get into the action than a 1 piecer. I am a loyal LEUPOLD scope user at least for the past 35years anyway. LIFETIME guarantee. I 110% suggest getting ANY Leupold even a used one in 4X or a 2-7, 3-9 or my personal favorite for a light or medium rifle the new 2.5-8X models.
Both Savages and Rugers are good quality. I do not like Rugers for personal reasons, though have owned a bunch of them.
Now to really screw you up.....on both of my African hunts I took two rifles, one a M70 and the other a Rem 700. Tough to pick between the two!! Here at home for antelope, deer and elk, I take the Rem 700 for a few days then grab one of the model 70's for a few more. Both are fine.
Good Luck....... Frank N.