The electric is a more complete instrument - Meaning that one can play both single line solos AND chords for accompanying other players or voice.
The electric guitar is also easier to play (and therefore easier to learn on) because:
- The neck is both narrower and thinner (making it easier to get smaller hands around)
- The strings are thinner (making them easier to press down, less wear and tear on the fingers, and much much easier to bend when soloing)
While everything that one can play on the acoustic guitar can be effortlessly transferred to the electric guitar, soloing techniques in modern musics require lots of bending - pretty much the exclusive realm of the electric guitar.
On an acoustic guitar, while bending strings is not impossible, they require ten times more strength, and will literally tear your fingertips to pieces as well as the danger of causing arm cramps that can easily become tendonitis or carpal tunnel syndrome.
There are, of course, stylistic concerns.
For example, Classical Guitar is usually played on a nylon string guitar, which is not the same look, feel, technique or sound as either an acoustic guitar or an electric guitar (and there is no bending involved).
If someone has zero desire to complete their guitar education with a working knowledge of how to improvise solos, in say, Rock, Blues, and Jazz, et al, there is no reason whatsoever to purchase an electric guitar.
For the record, it is actually easier to improvise solos than it is to effect chord changes!
That is because, when soloing, the guitarist is only playing one single melody note at a time with one single finger, whereas when playing accompaniment chords one has to be able to move an entire handful of fingers to a brand-new position in the blink of an eye every few beats or so.
It's a lot harder to move 3 or 4 fingers simultaneously to arrive at the next chord down the pike than it is to press one single finger to fret a note and then move the next finger to play the next single note!
I never ever knew that until I started teaching!
Like most folks, I always assumed that soloing was way more difficult (because it's flashier) and that bashing out chords was easier (because everybody knows how to do it).
That was a huge revelation for me, both as a pro player and as a teacher!
As regards pricing, there is no significant difference between purchasing a decent acoustic guitar and an entry level electric guitar package (which always includes a small practice amplifier, and usually some other goodies too: tuner, strap, gig bag, picks, etc).
Both can be had for just under the $300 mark.
Given the choice, I always try to steer my students towards an electric guitar since that will enable them to one day become a complete musician, whereas an acoustic guitar will limit them to only being a rhythm player.