I love the simplicity of 3-9X40 scopes. Plenty of magnification for any game coyote and larger out to 500yds. I love watching long range hunting videos, but the more I practice shooting out to 500yds the more I know it's beyond my ethics for big game.
I appreciate having a 4-12 when sighting in and know I wouldn't be happy with anything smaller past 500yds. Stay with a 40mm as with the scope mounted lower you will shoot better. Also, there isn't the science nor the practical evidence to support a larger obj.
The 4-12 is definitely worth an extra $100, but it's just enough magnification to screw you up on close shots if you forget to turn it down while walking around.