What are you going to be using this rifle for? Target, Hunting, ??
I love of both.
But I really appreciate the efficiency of the 308 Win. I haven't owned it in a Handi, so I can't speak from experiance, but I do in my XR and love it. For a target rifle the 308 is still a great choice.
I have used a 30-06 in a Handi, and loved it. And have taken game with it no problem at all.
I have one actually in the works right now. It's a good caliber in a Handi.
In a -06 I prefer the heavier 180 grain bullets, as thats the turning point to an advantage of the extra capacity. But both are very versitile and the 30 cals have excellent bullet choices, thats for sure.
The price of factory offerings don't differ much either between them both, as both are among the cheapest high power centerfires to shoot.
-Aaron