Ask any ole' timer; what is a "goose gun" and see what they tell you.

I'd opt for the 12 gauge. Stores usually keep a much better selection of 12 gauge ammo on the shelves in any length, be it 2 3/4, 3, or 3 1/2 inch. Same goes for choke tubes.

Both have the same amount of pellets and they both are going the same fps... Weres the advantage???

I have both... The only difference is the 10ga weighs a lot more...

All BS'ing aside. I have done pattern testing where we have loaded the same charge in both 10 and 12 ga, 2oz of 6's and 5's, fired side by side targets at equal distance with equal chokes, full. The 10 more times than not out performed the 12 with a standard bore diameter.
NOW. Throw in an overbored barrell on the 12 and things change, AGAIN!!! They performed almost identical!!!! A 12 ga with an overbored barrell is the same diameter as a 10ga.
Then throw in a Turkey designated choke for either and we are off to yet another race. So you go from a 10ga bore diameter to down just that of a 16ga and and it really starts to get interesting. The 12 choked down to almost that of a 20ga. The big trade off is weight, recoil, and price of shells. Not to mention another weapon. So you can do the math of all the above and those who replied as well. I will stay with my 12ga 3.5's and not have to worry. Just change choke tubes.

I suspect that many people have never had an opportunity to shoot a 10 gauge and so it would be difficult to vote a 10 over a 12 if that's the case. I have shot quite a few turkeys with a 3.5 12. I started out with a Mossberg 835 3.5" 12 gauge. Thing kicked like a mule even with a new recoil pad. And after shooting it (even with only 1 shot) it would give me a headache (not kidding either). Dumped probably 10 birds with that thing over a 12 year period and I don't remember ever not killing the bird dead in its tracks. I would limit my shot to around 35-37 yards max with that gun. Beyond that the pattern became erratic. After a while, I got tired of getting kicked around by that gun and the headaches it caused, so I sold it and bought a Browning Gold 3.5" 10 gauge. I can tell you that it was the best thing I ever did. Now I can reliably shoot 42-45 yards (with an aftermarket super full turkey choke), and like with the Mossberg, I have never failed to kill the bird I am shooting at...all with one shot. So while I would vote the Browning the hands down winner for my gun of choice, both of the guns have equal kill results. And after all, isn't that what we all want in the end?
Moral: Pattern your gun with as many different types of shells and pellet size as you can afford. I have found that only a very few shell types and shot size pattern well in either gun. Use of any other shell in a hunting situation might very well have resulted in a missed opportunity and possibly a wounded bird. And if that happens, we are likely to blame the gun when in reality it was simply the incorrect choice of shells.