The issue with the pre 2007 Remington/Walker designed trigger are very real. I wouldn't own a 700 series rifle made between 1946 and 2007 unless the trigger were replaced with aftermarket. This flawed trigger design resulted in over 100 multi-million dollar lawsuits that Remington settled out of court. Remington also settled a multi-million class action lawsuit over model 870 and 11-87 barrels splitting back in the 1990's. This is really what killed Remington.
Paying lawyers to defend them, paying off plaintiff's, and repairing millions of rifles returned to the factory left no money to put into R&D and led to cutting corners to save money on production. Remington redesigned the trigger starting in late 2006 but due to an error during assembly adhesive dripped into the trigger assembly on some guns between 2007 and 2014 which resulted in a massive recall. This is a safe trigger design, but still a costly error on Remington's part.
There are some design features on Remington 700 series rifles I don't particularly care for such as the extractor and the fact that they solder the bolt handles on, but in reality those rarely cause problems. Once the trigger issue is dealt with MOST Remington bolt rifles will be just fine. I've had several over the years, but currently only have one. I rarely use it anymore, but it was my 1st rifle purchased new in 1975. I've moved on to other rifle designs I like better, but keep this one for nostalgic reasons.
Savage has a well earned reputation for making accurate rifles at reasonable prices. I've had 3-4 over the years. They shoot well enough, but I just don't like many of the design features. I wouldn't have a Savage in a long action as a gift, they are loooooong. The short actions are still longer than other short actions, but are tolerable.
This is a close one for me, a toss up really. Neither Savage, nor Remington is currently making anything I'm interested in. If possible my answer is neither. There are a handful of older Remington's that I like well enough. I suppose it would depend on which individual rifles if forced to choose between the 2. It's not that I think either brand is junk, I just prefer others better.