I'm a big fan of middle bores... Used 350 Rem Mag a lot, and love 35 rem, 35 Whelen and 338-06. I've never used the 338 Federal, but I really like the round. Forget all the ballistics tables and published info on "ft/lbs energy". The formulas used to calculate energy tend to weight velocity. Fast rounds look good. However, middle bores tend to have hefty bullets, and use mass/momentum more than any ft/lb energy calculation really shows.... And impact speeds are usually modest, so there isn't as much shredded and mangled meat.
I do find that there is one disadvantage to these rounds... initial muzzle velocities are modest, and these bullets aren't super streamlined. When you get out to 300 yards, they've slowed a whole bunch. And while speeds and energy and momentum are all there, sometimes you start to approach the lower end of the expansion window for the bullet you are using. Example: My 350 would launch a 225 Nosler Partition to 2650 fps or so. At 300 yards the impact speeds are down somewhere around 2000 fps (off the cuff estimate). By the time that bullet gets to 325 or so, it won't open up as dramatically as you'd like. And I saw exactly that.... I shot a cow moose twice at a laser ranges 293 yards. First one was a shot that impacted the hinge point of her jaw, the second one centered the lungs and heart. It dropped her in about 40 yards. Expansion wasn't great. If I hunted BIG game in an area where shots were always under 150 yards, I'd still use the 350. But game doesnt always cooperate, and sometimes the 250 yard shot is the only one. The 350 is gone, and I've replaced it with a 280 Ackley because I wanted greater impact speeds at longer ranges (but didn't want magnum recoil).
If you want to hit whitetails hard at 100 and 150, the 338 Federal is ideal. However, those 300 yard shots, while rare, are going to disappoint some. And there aren't a lot of really hard opening 338 bullets to load, so its not like you can use a light for caliber hard expander to make up for it. Most 338's are going to be designed for the 338 Win Mag, or even the 338-06. You're at a big disadvantage right at the muzzle because you are already at the low end of the sweet spot for expansion with a 338 Federal
260 freakin rocks. Its the opposite of the 338 in every way. Super streamlined bullets that fly far and fast. Because the bullets retain speed well, performance at 300 yards closely mirrors performance at 100 yards. Long skiing 6.5 mm bullets have great sectional density and punch deep too.
My take: Use it as a dedicated deer rifle and go 260 all the way. Its cheaper to load, easier to shoot, and very accurate. Then, if you want a hammer for BIG game, go buy a dedicated hammer. Get a 35 whelen or a 336-06. The higher initial muzzle velocities will give you better bullet expansion and punch at longer ranges.