Both grips are the same width.
The finger-grooves fall in the same location, but the G17's grip has slightly more material below the last groove.
The biggest difference is the "hump" on the rear of the grip. The G19's hump is slightly higher, and most folks with average size or smaller hands prefer the "feel" of the grip with the hump in this location. Folks with larger hands sometimes prefer the lower hump on the G17, but not always; when I let my son (6-3-ish) hold both, he chose the G19 over the G17.
If you can arrange it, try to hold both one-after-another at the same shop; that will make it easier to choose.