There is really no advantage to the 300 H&H except for the romance of it's past history and use all over the world during the more glamorous days of big game hunting. It'll give more velocity than the 30-06 but less than the 300 Win Mag. Case life will probably be shorter due to the body taper which will probably allow more case growth and more frequent trimmings. In spite of this I still often think about a Ruger #1 in 300 H&H that I passed on several years ago.
I've never liked the larger 30 calibers much since smaller calibers will get the job done well for deer with less recoil but the 300 H&H calls to me for the reason mentioned above. The gun writers of the past that I grew up reading used it back when big game hunting was more than a score for antlers - it was an adventure. Owning a gun linked to that time period lets us connect to that in some small way.
I'd not hesitate to get one if the chance came along assuming you load your own ammo. If not, ammo cost and availability could be an issue unless you buy way in advance of needing it. I'd assume anybody who owns a Pre 64 Model 70 Super Grade loads their own.