I'm not the OP, but I'll give some reasons from personal experience...
First, the quality of the light is markedly different. This is primarily because of the much longer "burn" time of bulbs. At the shutter speed you choose you get the same exposure effect as natural sunlight because the light is present during the entire time the shutter is open. What you don't get is the strobe effect of ultra-high-speed xenon flashtubes producing maximum, clinical sharpness at 1/10,000-second bursts of light. Click (there was a url link here which no longer exists) for an example of that maximum sharpness. The platform was in free fall at the moment of exposure. Such sharpness is appropriate for some subjects, but not for all.
Second, using bulbs allows you to vary the GNs by varying the shutter speed. The higher the shutter speed, the lower the GN, because of the lower slice of the total bulb output that is caught on the film. Electronic flashes which implement a "power ratio" feature can simulate that same performance. But not all units have this feature.
Third, the output from portable bulbs is generally higher, and in most cases
much higher, than portable electronic flash units. Studio lighting trumps this, but with all of the disadvantages of equipment bulk and weight. The lowly Sylvania Press 25 and its cousins are rated by various manufacturers between GN 200-240 (tungsten, in feet) for 1/100-second shutter speeds at ASA 100. This surpasses just about all portable electronic units, including the monster Sunpak 622 Super handle-mount. (Rated by Sunpak at GN 200, but like almost all portable electronic units is actually a little less than that in the real world.)
Fourth, when paired with older (antique?) cameras, bulbs affect almost total compliance from potential subjects. Most have never seen them, let alone seen them work, let alone been photographed by someone using them. It's like an amazingly alien magic trick to most. I always reward my subjects with the offer of either a scan or print,
AND the used bulb popped from its reflector (after it cools). I suspect many are more interested in the burned bulb than the photograph it made possible. Go figure...
Fifth, and not least important, the display and use of ultra-cool vintage flashbulbs and equipment is a highly effective chick magnet. Mostly because the guys are way too embarrassed to admit their ignorance about them. And the girls are often genuinely curious, and not afraid in the least to just walk right up and ask questions.
Ken