Another important factor regarding the quality of light is the reflector shape and size.
Most portable electronic flashes cast light that is highly directional, designed for maximum throw. The reflector size is smaller than flashbulb reflectors, and is rectangular rather than round, giving a "shaped" throw and a sharper more point-source effect. Light is projected outward with less bounce within the reflector and less diffusion.
The round flashbulb reflectors are larger for the amount of light put out, are usually deeper and are curved differently.They create a larger light source to begin with, which gives a nicer look. The full conical shape of the light coming from a bulb reflector means there is more reflected fill from below and above if surfaces are reflective (if there's enough distance to allow reflected light to hit the subject). Flashbulbs put out enough light to give reach yet provide a softer light with more gradual edge cutoff, especially true with bulbs that mount with their tops pointing toward the subject. It is a treat to look at old news photos and see the different quality of the light, including daylight fill.
That's why the (discontinued) Sunpak 120J is in such demand. It mimics a flashbulb setup with a large round pebble-grain-finish reflector and a round bare "bulb" in the center. It's a nice unit, with the reflector movable forward and back for regular or wide angle coverage plus bounce and swivel, and multiple power settings enable a longer flash duration. It's the closest I've seen to a flashbulb setup, nicer than most diffusers or bounce reflectors, IMO.