Well a couple of things:
since you mentioned elk, I'd go for the 130 TSX. I have a habit of telling lots of shooters that with the Barnes bullets you can go lighter because they flat out penetrate like crazy. That said, I'm referring to calibers a bit bigger than the 6.5mm. As an example, I'd take my 270/130 TTSX or TSX out for elk anytime anywhere. They both shoot so well in my 270 I'd take a 400 yard shot or under but not further. My personal opinion is that the Barnes bullets are good for certain calibers within certain ranges if you want them to perform at their best. I just have a feeling they won't open up like they should when you start pushing those longer distances, unless you can place that bullet in the scapula every time.
The 120 will certainly work, but it's my opinion that you will want to hit an elk with all you can with that bullet diameter. I've got quite a bit of experience with the TSX and TTSX in several calibers and rifles. Many of my bears/deer/pronghorn have fallen to the Barnes bullets for me and others I load for since 2003.
The other thing I really like about Barnes bullets is they seem to like those max loads really well. I've got a couple or more that are 2-3 grains over Barnes' tested max and they are still safe in my rifles. I have a 130 TTSX moving over 3150 in a 270. We've not clocked the 110 TSX or TTSX in 3 of the 270s we shoot but we just look at the trajectories on targets and say to ourselves, "the **** is moving fast."
I think most of mine, regardless of caliber, are seated right at .050 off the lands.
Good luck with your choice. I'm telling you, inside of 300-350 yards, bullet tip and base do not make a big difference. Someone may chime in and tell my I'm full of hooie but I could care less. I've got enough experience with flat based spitzers at game at those ranges and we're talking an inch or two off from boat tails.