Welcome to the Forum
With these as the only two choices, I would purchase a 610 in a heartbeat. But then, I have never been a fan of the 44 Magnum.
I own a few 44 Magnums because I collect Smith & Wesson
But I am not making this purchase, you are.
Since you did not tell us you are hand loader, I presume you are not.
With that in mind and again with these as the only two choices, I would recommend that you purchase a 629
A selection of 44 Magnum ammunition is on the shelf of any retailer in any town of the US. That can not be said about 10MM Auto ammunition
Now, if we can go outside of your two choices, like many others I would recommend a 357 Magnum. The cartridge is beautiful for paper punching, there are lots of 38 target loads geared toward to organized competition and of course, there is always full power 357 Magnum.
Plus, as you can see modern 357 Magnums are available in an 8 shot variety