I own three Savages: two Model 12's, and a Mk. II in .22LR. All three have served me well, right out of the box. I have never owned a Remington, but only because I've never had the opportunity, not for any other reason.
That being said - my brother had a problem with his Savage - a Model 10 in .243. It was getting blisteringly hot, after firing four rounds, and the groups were minute of barn at best. Initially, when he called their technical support to request some assistance, he spoke with a very friendly person on the other end of the line. His suggestion was to ship it back to them, and they'd take a look at it. The person definitely agreed - something was not quite right.
Fast forward to 2 weeks ago. The rifle shows back up (it was gone for 2 weeks), with a note in the box indicating they couldn't find anything wrong. When he called Savage, and asked to speak to the technician, they balked at the idea and said it's not customary for them to do that. When he pressed on, they then said they didn't have the ability to transfer the call to the shop area. When he asked for a direct phone number, they declined. Same thing with an email contact. When he finally did blow a gasket with the customer service rep., the gentleman said "what do you expect it to do? It's not a bull barrel..."
He was furious to say the least, and called me up to say he had bought his one & only Savage.
A few days ago, he took the rifle back out to his range. Using the remaining rounds of ammunition from the same factory Remington Core Lokt box, he began to re-sight the rifle in. 10 rounds went down the pipe, with nary a hitch. By the time he tried his second box, he was posting 1" groups, at 100 yards.
Neither he nor I can figure out what the hell it was that was causing the problem, but it has obviously been remedied. Whether it was something Savage fixed, and didn't want to say, or whether it just 'worked itself out', the end result is it's fixed.
His customer service interaction the second time around though, leaves much to be desired. I kept thinking to myself all along, that surely Savage must have some sort of intermediary warranty company doing customer service work for them - but this appears not to be the case, as he dialed the same phone number from the company website, and from the packing invoice both times.
I love my Savages - but I have to remind myself, that not every company out there can be like Dillon Precision, and RCBS. It's a shame. YMMV.