I've got all three. Had several 7mm's over the years, have one 300, and a couple of 338's.
The 7mm Rem Mag is a favourite of mine, it offers exceptional performance in the field. For the type of hunting I engage in, it gives up nothing to the 300 Win Mag. The 300 Win Mag is the benchmark by which most magnums are measured, it will easily do what most of us need our rifles to do (obviously more than I've needed yet). Having said so, I've found that the 338 Win Mag measures up very well and I prefer it.
As a result of contemplating a thread that was posted a little while back, I have concluded that if the day I had to part with all but two rifles ever arrives, I'd keep my Dakota 76 in 338 Win Mag and my Sauer S202 in 270 Win. But man that would be one sad day.