Favourite would depend on the circumstances. Is the plains game hunting conducted during a dangerous game hunt as well? Then my answer would be different.

First my simple choice for the survey is:

1. 8x68S
2. .450 NE

But not for the survey but as part of a discussion if plains game is hunted along with dangerous game, I would choose:

.375 H&H Mag
.450 NE

The above allows redunancy. If the double is not being held, th .375 will work fine. If a scoped shot is needed, the .375 is also available.

A good standard choice has been named several times and these I used as well. My first plains game hunt, a single .30-06 was taken. For my capd buffalo and plains game hunt, I took just a .375. I might substitute a .404 these days if I wanted a small amount of extra grunt.

.30-06
.375 H&H Mag (or .404)

Due to weight considerations, I have always only taken one rifle except for one hunt when I took a 9.3x74R DR and a .450 NE DR. But I borrowed a 8x68S off Karl Stumpfe to try it out. So I would be comfortable with a .375 H&H Mag for everything, and if a .375 Flanged double with a scope, perfect.