"big bore" is a nonsense term. .243 is "big bore" compared to .17 Rem, and .348 Lott is "big bore" compared to .243, etc.
There's no definitive number or magic diameter that makes a rifle "big bore".
In pistol terms, lots of folks say the caliber has to start with a "4" to be "large caliber" but a .40S&W pistol has nothing on 9x25 Dillon, for example, or even .38 Super.
So the term is nonsense and relative from one discussion to the next. In my collection it would be 45/70, but before I had that it was .32 Special, which was a monstrous thumper compared to most of my other rifles.
Maybe we should talk "big bore" in terms of bullet weight. Anything over 210 grains, in most collections, is a whopper.