I have the opposite problem from VoodooMountain. Since Glocks have a grip angle that has to be different from just about every other handgun except maybe a Steyr or a Luger P08, Glocks do not point naturally for me. Glocks also feel like a torture device in my hand, sort of like grabbing a brick. The Gen 4s are a little better in that regard, but the grip is still just too squared off for my taste and I don't care for finger grooves on the front strap. The stock Glock trigger actions seem to me to be spongy with a somewhat indistinct reset. And the stock plastic sights are pretty crappy.
Now having said that, I have shot G19s and when I have I have gotten them to perform better than I might have expected. I appreciate that the design is time-honored and simple to work on and modify. Magazines and many other parts and accessories are cheap and widely available. The sides of the slides are very "clean".
The SIG P320 is a new design. SIG has had a few problems with the roll out and has modified the trigger, take down lever, and slide stop lever in response to complaints. And the .45 ACP fire control unit turned out to be incompatible with the 9mm, .40, and .45 cal unit, despite SIG's promise of cross-caliber compatibility. The caliber X-change kits are too expensive to be a practical option for most people, and magazines are considerably more expensive than Glock mags.
Being a newer design, holster options and other accessories are still limited, but the P320 has made quite a splash, it seems to be high in the running for the FBIs new 9mm handgun, and also a top candidate for the US Army modular handgun program, so I expect that will change very soon.
I have a full-size P320 .45 ACP and have shot a full-size .40 S&W P320. I have only handled compact and carry model P320s as yet, but I have shot 9mm P250s which have the same grip module.
Points in favor of the P320 from my point of view: the medium size grip module of the P320 full size and compact is markedly more comfortable than any Gen 3 or Gen 4 Glock I have yet handled or shot. The trigger action is much better with a much more positive reset. The pistol points much more naturally for me and I shoot it more accurately. I bought my full-size P320 .45 NIB with night sights and 2 magazines for a little under $500 delivered. A new Gen 4 Glock 19 with plastic sights (but 3 mags) would have cost me a few dollars more. Both the full-size P320 .40 S&W and the .45 ACP handle recoil extremely well and come back on target quickly, despite the "high bore axis" that Glock fans are always carping about.