Really, there is no right or wrong answer here. Either one will do the job just fine and both have great high capacity magazines and a ton of accessory and configuration options. It really just comes down to, how much do you want to spend? What type of configuration do you want to end up with and which one floats your boat the most?
A stock basic 10/22 will be cheaper then a 15/22 but if you prefer a pistol grip type config and the flexibility of a forearm that you can mount accessories on, the 15/22 might be the better path? (You can setup 10/22 like that too but it won't look as good IMO by the time you buy all the parts to set it up that way, it won't be much cheaper either)
Do you want a "tactical" style rifle or a sporter type? I love 22's and I love AR's but for some reason, a 22 cal AR's don't really float my boat? So for me, I prefer the 10/22 but if I wanted something more "tactical", I would get a 15/22.