So... this probably won't help at all, because I'm not exactly sure which I'd rather have of the two. Mostly because neither was my first choice for that purpose... But here are my scattered and unhelpful thoughts...
Comparing the rifles:
Comparing these two cartridges isn't complete unless you also consider that you're comparing long and short actions. If you're looking for a lightweight rifle, a short action Remington is about as light as you can build on - Sako, Winchester, Mauser, Ruger, and Savage actions are a half pound to a full pound heavier than the Remington 700. The 700 also gains less weight when you jump from short action to long action compared to other brands, so even in a long action, the 700 has the advantage in weight savings. Titanium 700 Ultralight is even lighter, if you can find one. Is lightweight just a buzz word, or is it your focus? If it's the focus, then the Rem 700 short action has the advantage. If it's not that important, then a 700 long is a good option too - still lighter than short actions from some other brands.
Comparing the Cartridges
I'm not sure why - and I'm quite certain I don't have a good reason for it - but the 270win just has never thrilled me. Maybe it's because I grew up with an '06 and my brother with a 270, or maybe because I got burned out by Jeff Coopers followers that were super closed minded to anything BUT the 270 with a forward mounted optic... I can't say anything bad about it, but I don't really have a hole where the 270 fits. I don't have a love affair with the 308win either - in it's case family, my heart belongs to the 7-08. For a 30cal, I find myself leaning towards the 300win mag over the 308 or 30-06, basically, if I need 150-180grns, then I can justify the horsepower, mentally.
If you're a subscriber to sectional density based rankings, like Winchester's CXP rating system, or a Chuck Hawk's fan, since he follows that program too, then you can consider that the 270's 140grn fodder is really a lower end CXP3 bullet, whereas the typical 150's in the 308win are mid to upper end CXP2 bullets for sectional density. Alternatively, the 308win has about a 10-15% edge for Taylor Knock-Out Factor... More impact vs. more penetration, to which philosophy do you subscribe?
Barrel length and overall length might be a consideration, depending upon model. 308win can burn powder well in a 20-22" tube, the 270win's larger case and smaller bore usually benefits from a 24" tube. Then add in the extra action length and the 270win might be a 2, 3, or even 5" longer rifle.
What I did, not that it matters:
My personal "mountain rifle" has been a 7-08 Rem 700. Despite the extra action weight, I'm working on a takedown mountain rifle, also in 7-08, but on a Ruger M77 action - using the Ruger because of the integrated recoil lug, rather than a sandwich type (although I might be changing my mind about that). I also hold a soft spot in my heart for the 284win, and it brings a little extra horsepower over the 7-08, although I'm internally conflicted about putting it in a short action - so that's a decision yet to be made.
Which I would pick - just between the two:
If weight matters most, Rem 700 308win. If weight isn't the top priority, then I'd go 270win.