I have (had) both. For a hunting rifle I like Rugers - 3 position safety, controlled feed, long Mauser type extractor, except for magazine box all parts are relatively durable investment castings. I like the Ruger scope rings because ring/mount tightness can be checked out without removing the scope from the receiver and scopes can be removed and then mounted again with no or almost no readjusting.
My Ruger complaints are the triggers are heavy and creepy but that can be changed with a trigger job by a checked out gunsmith or knowledgable other. I don't like the diagonal bedding screw arrangement because when epoxy bedding the rifle action much time and effort has to be spent in refitting the trigger guard and floor plate.
As for the Remington - there are many stocks available, mounting systems, and should you decide to restock the rifle they are easily bedded because of the round receiver. Some of my very most accurate rifles are Rem 700 SA's.
I have had problems with Rem 700 extractors (finger nail type). The Rem 700 bolt is not as easy to field strip as the Ruger. Rem 700 use a dime in a slot to hold the cocking piece back. Ruger M77 use a small allen wrench through a hole in the bottom of the cocking piece to hold the cocking piece back.
As much as I like the Ruger for a hunting rifle I think my FN Mausers are tougher and more reliable. Specifically the ejector arragement - I have had R M77 MKII's crudded up with a combination of dirt, rust, and gummed up oil to the point where the ejector would not snap out of its slot. Try cold temps, salt water, mud (Alaska) and this can happen faster than you would believe. The Mauser is easier to clean up without taking the rifle out of the stock. No, my Mausers don't have a big washer inletted into the side of the stock to help me strip the bolt down completely.