Back to the original post. You are looking at a 30-06 over the .308. Both cartridges are good accurate rounds. Both can be handloaded using the same bullets. But, the .308 is always just a bit slower, and can't push the same bullets with the same velocity or energy as the 06. The 30-06 is always just one step above the .308.
My first rifle after I left home was a Parker Haile 3600, in .308. That was in 1971, I carried that rifle till 1985. I killed lots of differant game, close and far with it. Still have ity in my vault, and will someday give it to my oldest son. In 1985 I bought my first 30-06, haven't shot the .308 since. Like being able to use the heavier bullets, with decent velocity.
Now as for the Savage 110 V the Handi. I have both in 30-06. My go to gun is the Handi, but my second is the Savage. It's not a question of accuracy, both shoot just as good. I can bust a milk jug at 700 yards with both. I can reload and shoot a second shot just as fast with one as the other. It's just a matter of preferance, and I've owned and carried the Handi a lot longer than I have owned the Savage. Both guns need trigger work, both guns need tweeking to get them where you like them. To me they are comperable. BUT, and this is a big BUT. The Handi you are looking at will in most likelyhood be an extractor, not an ejector. Scratch that reloading bit. No way a new Handi can even compete with a Savage 110 on getting off a second shot. Having to reach down and pull that empty, then drop in a new round just takes too long. So the bolt action is going to be faster on a second shot. Unless you are hunting dangerous game that should not be a concern, I hunt dangerous game so that is a biggie to me.
Otherwise, it is which ever one you feel more comfortable with. One good test I always performe when looking at a gun. Close your eyes and shoulder the gun. Then open your eyes, you should be looking right down the top of the barrel, or through the scope. Do this three or four times, and be honest with yourself. If you do not shoulder the gun properly, where you are looking down the barrel or through the scope, without adjusting each and every time. Pass on that gun and continue looking.