If you had to choose between the two, what are you going with & what model? Home defense/general safety that won't be used for concealed carry.
The biggest question is what caliber do you like? I will assume 9mm, because that the "me-too" caliber of the day. 9mm hollow-points will not over-penetrate, so I will propose a 9mm in an auto loader.
Sig - 320 is a great rig, the older 220 is nice, but it is huge. Many people have an issue with it in their hands. I have a 365 that I am in love with (especially after adding a Wilson Combat handle). I am a 1911 guy - that is what I learned with. Sig makes some awesome 1911's. They come in 9mm, 45, 10mm. Of the 2 brands you listed, I would steer you toward the 320.
Glock - Utilitarian. Poor grip angle. Poor trigger. Goes bang on a regular basis. It is ok, but there are better, for less money. Glock 19 is sized nice. The Model 20 and 21 (10mm and .45 respectively) are a little bigger, and medium and small hand people may have some issues.
I will add Barretta 92F. Good capacity. Popular. nice balance. 9mm
On the budget side, Girsan makes an excellent clone of the Browning Hi-Power in 9mm.
If you are not a firearm-person, and do not do a lot of range-time, I recommend a .357 - Smith and Wesson is my preferred brand. You can shoot .38's or +P .38's if you do not like the full-load .357. Wheel-guns (revolvers) have less to go wrong than a semi auto. The old saying is "they just go bang". A Smith and Wesson 686 plus (7 shot) is a wonderful shooting tool. No magazine issues or feeding problems with a revolver. Especially if you may have it set for a long time in the dresser drawer.