Both makes and models are quality firearms, each with their own pros and cons, depending on your opinion. Ultimately, go with the one that fits you best, in the version that provides you the features that are important to you.
I have owned, shot and hunted with both, and have had decent to excellent accuracy in both, depending on the individual rifle and its preferred ammo/handload.
As a lefty, Remington has offered me more options over the years, as well as more availability for customizing to get exactly what I am looking for, and therefore I have and owned more 700's over the years. I do not have a 70 at this time, for these reasons. I do wish that FN had produced a LH 70 while they produced rifles in the US before moving production to Portugal, as the fit and finish on these rifles was very good, and the wood was very nice. (I almost bought a RH Super Grade w/ French Walnut as it was an absolutely beautiful rifle! If only it had been LH!!!)
(Both my custom DG rifles (376 Steyr and 416 Taylor) are built on LH Ruger M77 Mk IIs in SS/laminate as they were what was available at the time of the builds, although I would have been just as happy with a 700 or 70 if I had been able to find a couple donor rifles at the time)