As you say the head of the TK22 is indeed larger than the TK15. Whether this is an issue it will depend how you intend to carry the light.
If you want to carry in your pants' pocket, then the TK15 will be a better option.
Build quality goes: both lights are on par - same Fenix TK series.
UI: is identical as far as I understood. The TK15 has a stepdown after 30 minutes the TK22 after 22.
Runtime: the TK15 will have 20 or so minutes longer runtime - if that's important for you, take into consideration.
Brightness: the TK22 will be brighter though visibly less than the lumen difference on paper might lead you to think.
Throw: the TK15 will throw a bit further but not by much.
Beam: I think the main difference lies here: if you prefer a throwy kind of beam while the TK22 will be floodier.
Overall there is no better between the two lights, I would just choose the one that fits your needs better based on beam and form factor.
Just an advice: I would change the thread title from "TX22 vs TK15 S2" to "Fenix TK22 vs TK15". Adding the brand name and correcting the flashlight name is going to make your thread more visible and get more replies.
You can change the title by clicking on "Edit Post" and then "Go Advanced" on the bottom right corner of your screen.
I was curious so I also checked the head diameter of the TK15 and TK22: it's 34mm and 40mm respectively so just half an inch. It's not a big a difference if you carry it in cargo pocket, holster, or bag.
You can also see brightness levels and runtimes below - Fenix are generally really accurate.