I'm a Model 70 fanboy. Stronger action, better quality, and overall more robust. Plus I prefer controlled feed to push feed on pure hunting rifles, but that's me. Remington 700 rifles made before 2007 are nice, which was before their QC hit the tank. If you wanted to build a custom rifle, then I'd recommend the 700 over the Model 70 as you can take the action and do whatever you want with it.
A lot of people mention Tikka. They are very good rifles for the money, but only to a point, IMO. Under $800 I don't think you can beat a Tikka, but once you get to that $800 - $1,200 range I don't think the Tikka is the bees knees anymore as it starts competing with the Model 70 and Browning X-Bolt, which IMO are both better rifles. The Model 70 has a more robust action, better overall quality, and has an MOA or better guarantee which is more than enough for hunting. And if they still made them, I'd recommend the CZ 550 as well. The actions are a bit gritty out of the box, but boy oh boy are they strong and do they feel rugged as hell.