You pretty well nailed it, altho I wouldn't say the 6.5 is a flatter shooting cartridge. When zero'd for 300 yds/meters/paces (whatever) like my Old Swede Mauser is, it tends to shoot a might low at 100 yds(understatement there) so there's plenty of arch in the old round.
Since you're going new Win Featherweight and I assume are in the USofA you'll probably be able to pick up .270 with a little more ease at any store that sells ammo, than the 6.5SE.
But, if you ever do get a chance to pick up an old Swedish Mauser in 6.5, do yourself a favor and snag it. You won't believe what a really old gun can do... why sometimes it even makes me look like I can shoot a little. And mine was made in 1900 somewhere in Germany
It ain't no featherweight and it's a might long and skinny looking and the knob sticks way out to the side... but boy, does that thing shoot well. I reckon if I was to go bear or elk hunting and got up close enough to use the open sights and placed the round where it ought to go, a black bear or elk sized critter would eventually expire pretty darned quick using the 6.5x55, with or without Jack Conner's stamp of approval. Now Elmer Keith would probably sing a different song and tell me I was undergunned for shooting moose at 600 yds (and he'd probably be right).
And I reckon if'n I needed to, I could affix bayonet and always use it as a Swedish Boar Spear... but I digress.
In today's world, you find more variety in the .270 loads. You don't reload. Stick to it for a new rifle purchase.
But you really can't go wrong either way.