Depends on where you are approaching Mexico 15 hwy from. If from the east it might be quicker from Douglas, but the roadway may not be as good for you, as the one out of Nogales.
For a time folk from the west often went across at the Lukeville/Sonoyta crossing. But in time we found out that the paperwork that needed to get done always seemed to have hangups, causing some major delays. Many that we knew, and that included ourselves, would thereafter enter Mexico from Nogales. Things have changed at the Sonoyta crossing, with the place to stop and get paperwork done moving closer to Coborca, pretty well eliminating the back-tracking to the border crossing which meant a 50 km trip (the copier had run out of ink at km 26!) out of eight of us, four had to return to the border for copies, and two had to return to obtain US dollars to pay, when the only card the man had would not swipe and he could not use his wife's Visa card because he did not have their marriage license!
Nogales never had surprises for us, maybe a short lineup, but that was it. What Douglas is like I don't know, never crossed there, but if you are coming from Tucson, or Phoenix, you might as well cross at Nogales. The road from Douglas is a bit longer, and unless you want to check out Tombstone and Boothill,and Bisbee, Nogales could be your best bet. In fact, there is a good road the runs from near Tombstone through the bird watching country of Patagonia to Nogales, AZ, USA. Also, if you overnight on the US side, you could meet up with fellow travelers who want to get an early start and so they will stop overnight at, say, the Nogales Walmart on the US side, or at the Desert Diamond Casino just south of Tucson. Good luck and safe travels!