I consider big bores to start once you get past .375", using the bore diameter as a measure instead of case capacity.
No doubt the .300 WinMag is a powerful round, and I consider it a big case but a mid bore.
Just my thoughts on it.
I've used rifles in .348, .444, 44 mag, and .45-70. Though the .348 is a mid-bore, it is powerful!