SDYOTE:
There IS a sense of accomplishment from calling in a coyote with hand calls! But you asked if an e-caller will call more coyotes than an experienced hand caller. I feel sure there is no absolute or “works-every-time-everywhere” answer to that. With both kinds of calls, the types of sounds, duration, and volume variations introduce thousands of variables. And there could be many coyotes near you or none at all. Terrain and vegetation can make a big difference in whether or not you even see a coyote that moved in close and then left. Weather and time of year add a bunch of variables. And so many more . . . . . .
I feel that the biggest advantage to an e-caller is that the source of the sound is not where you are. You can place the caller 30, 40, maybe 80 yards from you, focusing coyote attention there rather than right on you. After 10 years of calling, you know darned well that a little movement on your part can spook a coyote that is looking right at you (the source of the hand call sound). Think of your experiences and where it might have been nice to have that sound source coming from an open, ‘shootable’ area away from you.
TROYR and BERETTAMAN mentioned using e-calls and hand calls together. In rolling open calling country, especially in the earlier part of the season, I think that’s a great idea. Often, i turn on a LOW VOLUME distress sound, hoping to interest any “near by” coyotes. After a bit, with no observed response, I screech/scream loudly once for several seconds with a high-pitched Crit-R-Call (mouth blown), hoping to engage the interest of a far-away coyote. During the setup, I let the e-caller run continuously on LOW volume. The theory or hope is that a long-distance coyote may hear the screech and head my way, and when he gets close enough he hears the low volume distress and focuses on it. It works, but, as you’d guess, certainly not all of the time.
If you want howling to sound like multiple coyotes, you can run an e-caller howl simultaneously with mouth-blown howls. But I’m not sure you’d want to leave an e-caller howl running indefinitely.