An old rule of thumb is about 1 x per hundred yards on big game. But there is leeway and preference.
And we all have preferences.IMO,our shooting irons are one place in life where we get to have our preferences.No need to agree.
If I start with the pupil of my eyeball,it dilates to about 5 mm in lower light,7mm in dark.So,I don't lose much performance with a scope with a 5mm exit pupil,but 7mm is great.
A 6x by 42mm scope gives me a 7mm exit pupil. So does a 4x by 28. A 6X by 30 or a 4x by 24 are fine in any normal shooting light.
But as power goes up,objective lense size goes up. A 10X scope needs a 50 mm objective to provide a 5mm exit pupil. A 14X scope with a 50mm objective only has a 3.5 mm (approx.) exit pupil. In lower light,that is a bottleneck.
The tradeoff for higher power is ,among other things,bigger objectives,and therefore,taller rings.
When you bring your rifle to your cheek with your eyes closed,get comfortable,and open your eyes,you really need to be looking at a bright,clear,full scope field of view.
In MY opinion,nothing else is acceptable.
And,of course,those who have 56 mm scopes in tall rings prefer a 2X lower power because its easier to find the 2x field with your face up 1/2 inch off the stock.
For myself,on a rifle I built and stocked to fit me,I look at the target and mount the rifle and the crosshairs are on the target. No looking for anything.
That's with the 6X by 42mm Leupold that's been on my .257 for over 20 years.
If the 257 was an over and under with a shotgun barrel,I'm sure I could shoot pheasants with that 6X.
That scope is better than the naked eye in poor light.
I'm afraid Leupold may have discontinued exactly that scope,I think you can get a "wide Duplex"still,but the old standard duplex is ,to me,very useful for ranging and Kentucky holdover.
Variables are useful,and they make good ones.But ,for myself,my ballistics,my reticle,my ranging,is always exactly the same,every time I look through the scope.. Top hanging duplex post,dead on at 100 yds. Center,300 yds. Lower post,430 yds. Antelope fits duplex,200 yds. 1/2 duplex,400yds.
All instant,always the same.
I have a Boone and Crockett 3.5 to 10 X Leupold on a 308 AR. Almost missed my hillside with it when I first put it on the rifle.I used the reticle holdover at a lower power.I nearly overshot my backstop.
That requires a lot of extra thinking.That scope is somewhat chaotic if I use the variable.I always have to start with "Where am I at?"
A fixed X is like irons,You just shoot.
For myself,not anybody else,a 3.5 to 10X by 40 mm is the biggest scope I'd put on any big game hunting rifle,and I'd probably go 2.5 to 8X.
The last time I went antelope hunting,I used my replica 1903A4 with an old Lyman 2.5X.It did just fine.
Start with the rifle,scope,rings,etc fitting YOU in shooting position
I also like my rifles light,trim,easy to carry.
And get some decent binoculars. Using your rifle to glass the unknown is rude and unsafe.