I have both and have hunted with both. Here's my opinions.
10 gauge advanatges:
They tend to shoot a more even pattern. I find on average the pellets form a more uniform pattern with smaller blank areas than a 12 gauge 3 1/2".
They tend to have less felt recoil. 10 gauge guns are usually heavier than 12 gauge guns and that helps with recoil.
In my subjective opinion, 10 gauge is less ear splitting than a 12 gauge 3 1/2".
If you like rifled slugs, the 10 gauge rifled slug is nearly double the weight of a 12 gauge rifled slug.
10 gauge disadvantages:
Much fewer load choices, so much less versatility.
Tend to be heavier, in some cases, much heavier.
There are 10 gauge loads out there that are actually lighter than some 12 gauge 3 1/2" loads. I see no point in getting a 10 gauge unless you wanted to shoot the very heaviest loads available, or unless you just wanted one.
I think when it comes to very heavy loads, the 10 gauge handles them better than the 12 gauge.
And as far as just wanting a 10 gauge, that may be the best reason of all for getting one. I mean, how can you not love this?
Or 2 5/8 ounces of #9 TSS