I dont know how much sense this will make, but Ill try.
Assume a right angle inside corner. Assume youre running the same base mold all around the room.
Run one piece of base, square into the corner. Miter cut (45° angle) the end of the other stick. Use the line where the miter cut meets the bases surface as your cutting line. Thats faster and more accurate than scribing.
Cut along that line with a coping saw. Dont make a right angle cut. For the same reason you dont use an inside miter cut on in inside corner. Any junk where surface meets surface makes the joint gape. So
Use a miter box to get your line. Cut with a coping saw angled so that the curved edge youre defining is the first to touch the already-nailed-in base. Fine tune with a sharp knife. If you spend the day running trim, with a good finish bench, its a quick process.
Say I need to do a single inside joint. I dont have my coping saw with me. Ill make the miter cut and cut the coping joint with just a knife. Thats slower than using a coping saw. But faster than walking to my toolbox.
Most of the time on the job, my coping knife is my Stanley knife. If I need to cut tighter curves Ill use my Jr. Stockman.