Since you are looking for a quality bullet for mixed game you MUST choose a bullet that is adequate for the larger species. 150gr and 165gr bullets in the .30-06 are best suited for deer size game and virtually every traditional cup and core bullet will do the job. However moose are a whole 'nother beast and can easily kill you in comparison to deer! If using traditional cup and core bullets I would use nothing less than a 180gr bullet. Personally, I would choose a bullet design that retains the vast majority of its weight to allow for deeper penetration considering moose are a big boned and tough animal. The .30-06 pushes bullets fast enough that core and jacket separation will and does happen. I would look at the Barnes TSX and TTSX in 165gr and 180gr bullets. These bullets open reliably at both high and low velocities and penetrate like there is no tomorrow. You could also consider Accubonds, Scirroccos, Core-Lokt Ultras, Nosler Partitions, and Hornady's Interbond and GMX bullets. You may even want to look at Winchester's new Power Max Bonded and Federal's Fusion, BUT I would only consider the 180gr loads viable for this application. My personal choice to start with would be the 165gr or 180 gr Barnes TTSX or TSX in the VOR-TX line of ammunition, with a bent towards the 165gr TTSX.

Iv used the 06 for many years for both moose and deer i mostly used 180 grain winchester silver tips,the cheap winchester bullets.they work just fine so do the plain jane power points.moose arnt all that tough an elk has more will to live then a moose does.all this talk of needing a premium bullet is just a way to get your money.all though if i had the money for a guided hunt id probably dish out the extra ten bucks for premium ammo.whatever u use just put it where it counts and fire up the bbq

As for meat damage to a deer from a 180 grain bullet,theres hardly anny meat in a deers rib cage anyways but will leave u a great blood trail

What I do is find a premium bullet that expands in a controlled manner. I then work up 1 "pet" load that shoots that bullet extremely well. That's my 1 and only load for that rifle now. It'll usually be the only load shot out of that rifle and when using only 1 load/weight bullet you can memorize the trajectory easier. My choice of a bullet is the Nosler Accubond in 165gr weight. The 165 Accubonds will perform great on a elk or a deer. When using a good premium bonded (or solid copper) you can get by with a slightly lighter bullet such as the 165. Be aware that what shoots great in my A-bolt may shoot different in your rifle.

He mentioned he's using Trophy Bonded Bear Claws, a IMHO a Bonded 165 should hold up just fine. That being said, I'd prolly look at a Nosler Partition in 180 for Moose and something heavier if hunting in big bear country...

30-06 bullets
 

I use either good old Federal Power-Shok in the blue box or Remington CoreLokts both in 180 grain. I prefer the Power-Shoks because they are more accurate and IMO they hit harder. I tried the TBBCs once and the result was the only deer I've ever lost. It was too stout a bullet and went right through without opening. Hope this helps.