I too am a fan of the 7mm, and have a custom lh 7MM STW, a custom lh 280 Rem, a Winchester Model 88 being rebarrelled to 7mm-08 as we speak, and a Model 88 in 284 Win.
Hands down, the 280 Rem is my favourite cartridge, while my favourite hunting rifle for open country is my lh custom Sako AV in 7MM STW.
That being said, I looked for over 20 years to find a 284 Win, and finally found a very nice Model 88.
Haven't played with it very much yet, but am showing promise with the 140 gr A-Frame and will do just fine on the deer, bear, moose, elk and caribou!
Any real advantage over the 280? Not really, but a very interesting cartridge that has always been on my bucket list. Perhaps an edge in efficiency with the shorter, fatter powder column. So far, accuracy is not as good as in my 280 (or past 280's). But I have not yet tried AccuBonds (my favourite hunting bullet, and the easily the most consistently accurate bullet I have tried in all of my rifles, and excellent on-game performance) in the 284.
3 vs 5 rounds in the magazine = similar argument between the 7mm Rem Mag and 280AI. If in big bear country, nice to have the extra capacity. For other hunting, one and done should be the goal, but life does not always meet our goals and the extra rounds in any repeating rifle just adds a sense of security.
If you want to shoot longer, heavier bullets (ABLR's, Bergers, ELD_X or M's, etc.), I would load those in one of your 280's where it will be able to capture any gains you are looking for.
In the 284, stick with the 140 to 160 bullets of normal design (Nosler, Sierra, Hornady, Swift A-Frames, etc.)
In a short action for a mountain rifle, as much as I love the Remington 700, it has the shortest magazine box, so would recommend an action by another manufacturer if looking to seat bullets out a little further. For example, Winchester's short action magazine box is longer. Also like the Sako.
A friend built a 284 on a long action, but rarely uses the full length of the magazine well for his handloads. Without a block in the magazine well, the shells can rattle back and forth under recoil and batter bullet tips.
The advice above for a min barrel length of 22" is good. 24" will get you more of the cartridge's potential.