In theory there should be very little audible difference between an electric dryer and a gas dryer made by the same manufacturer. I personally would say gas makes a few dB more noise than electric because the combustion process itself is not totally silent. It's a lower frequency sound compared to the fan "whine" that is driven by the blade passing frequency at the fan housing cutoff.

That said, noise levels do vary between manufacturers, not much, maybe a few decibels. I believe every u.s. Manufacturer is about 56 to 62 dB when connected to a duct vented out of the room. 4 pole induction motors, which have dominated U.S. production for years all move very similar amounts of air.

A rigid metal vent can be quieter than a flimsy plastic vent line. Consider reviewing your vent line materials.

Laundryvet

The only difference that might make the gas one quieter could be a lower rate of air flow.
I've only owned electric dryers and they've always make a rushing air noise out the vent (along with hearing the dryer whine of the motor).