bushgun, you ought to be pistol whipped for even bringing this up. The subject has been beat to death not only on every "gun" forum since the birth of the Internet, but also in every "gun" magazine that's been in existence since the late fifties.
Jim_Dandy made a lot of good points about the current lack of quality in the parts, wood, finish, barrels, and workmanship on the current offerings from both Winchester and Remington. These are all valid points and worth taking note of.
Your original question, however was "Pre '64 or Remington 700 action". There is a huge difference between the current Model 70 action, "Classic" or otherwise, and a true pre-64 Model 70, and noone here has even mentioned the primary design difference (controlled feed vs. push feed) between the Remington 700 and the pre-64 model 70.
The answer to your question really depends on what you expect out of the rifle.
If you want a super accurate paper puncher, then go with the 700. The 700 action is stiffer, is more easily trued and aligned, and is inherently more accurate than is the action of the pre-64 Model 70. The 700's only real faults are its push feed design (it won't work if you happen to be hanging upside-down in a tree), its wimpy spring steel extractor (try finding a replacement for it in Dimebox, Texas on a Sunday morning), and its overly complex multi-lever pressed steel trigger and safety mechanisms.
If, on the other hand, you want a rifle that you can depend on in almost any situation, then the pre-64 Model 70 (which is really nothing more than a modified '98 Mauser), with its controlled feed mechanism, Mauser-type claw extractor, and its simple trigger and safety design is simply more likely to work, everytime, under nearly any condition you might care to subject it to.
Next time you're at a gunshow, look for a 92-95% Pre-64 model 70 (yeah there's still a lot of 'em out there) and closely compare it to a brand new Model 70 Classic or to a new Remington 700. If you know what you're lookin' at, you'll quickly understand why that Pre-64 is twice the price of the current offerings. It aint just "collectors value" either.
If you're stuck on the Remington, and it really is a fine rifle, try looking for an old Model 721/722 (long action/short action). These are basically the identical action as the current Model 700 and can sometimes be picked up for a song. I bought a 722 in 257 Roberts for $150 a couple of months ago. As usual, the price was low because it had a broken extractor and it was basically a non-functional unit. You'll want to refit any Remington 700 with a Sako type extractor anyway.
Aim straight . . . Doug