Going to scope my sons gun this year with a Leupold vx1.
Good selection. I've got a VX-I 2-7x33 on my 336. I like it. My only gripe with it is that the elevation and windage adjustments don't have "clicks". Eh, I can live with that.
We hunt a lot of thick woods and just wondering if the 3x9 40mm scope would give us a bigger field of view when looking and trying to first find the deer or trying to pick up a deer running if a second shot was needed.
Actually, the 2-7x33 has a wider field of view than the 3-9x40. The greater magnification comes hand in had with narrower field of view. This is a case of: Less is More. Less magnification means More field of view.
I have used a Leupold 3-9x40 (in particular, a Vari-X III on a Win 88 in .308 Win) in the past. Nice scope, but it bit me once -- the deer was way close (less than 20 yards, I was still hunting), and I happened to have it cranked up on high-9 and all I saw was a blur of deer hide. I did end up taking the deer, but the shot was, sadly, less than optimum. It went down DRT (literally, with powder burns), but I hit high and blew up some of the backstrap. :'( I was young. Lesson learned. Keep it cranked down unless you really need it. This is part of the reason why my 336 wears the 2-7x33. The other reason is that the 40mm scope will need to be mounted with medium height rings, where the 33mm scope can be comfortably mounted with low profile rings. On a 336, lower is better when mounting scopes. That's just what the geometry of the rifle demands.
What the 40mm objective gives you is the potential for better light gathering as opposed to the smaller 33mm objective. IMHO, it isn't all that much greater, and doesn't make up for the greater weight, higher mounting, and narrower field of view. 7x on the top is still plenty enough for still hunting at ranges even further than a 336 is capable - all the way out past 300 yards. And 2x on the lower end gives you a better field of view than 3x.