The Tikksas i have had were all shooters. One of my closest hunting buddies has been using a Battue in 30-06 for about 10 years now or more than I can remember and it has a fair few moose on it. Mine were 308, 6.5x55, 7mm-08. They are solid, trouble free and accurate rifles.
My experiences with Howa/Vanguard have been very good as well. They're a solid under $1000 choice.
Any of those cartridges will take moose with aplomb if you hit them well. 308 is just fine.
When shot with 300 WM, 30-06, 308 or 9.3x62, from what I have seen they all pretty much react the same. If its not a CNS hit, they run a lil ways and fall down. Results were practically indistinguishable, one between the other, and a follow up shot was often made, because there was time. The ones I've seen shot have a tendency to slouch around a bit and not light full afterburners like a deer that just got shot.
Very limited sample size, cause I've only been around the fellow a few times when he killed, a 270 Weatherby seems to really put a hurt on them.
My dad's answer is to shrug and say "guns a gun". He uses a 303 Brit, fwiw. But he doesn't take very long shots either.