Bullet design is more important than bullet weight per se.
If you match the velocity to the bullet you will be fine whatever you choose.
A search on my profile will bring up some load data and observations on various bullets and loads in my 06.
I've settled on a 180grain Hornady BTSP interlock for pretty much everything from muntjac to moose, with everything in between.
Loaded to 2500-2700 fps they drop anything suitable with decent placement and meat damage on smaller species is perfectly acceptable, about like Jonher describes.
For show and extra peace of mind I play with things like 200 grain Accubonds, 180 grain partitions and 168gr TSX but although I admit they penetrate better, they don't seem to kill much better.
For the first two years in the UK I used a 150gr Speer BTSP at 2800 fps ( 308 velocity ) and it did fine from muntjac to big rutting fallow buck, more damage than the Hornady though.