Acoustic amp for electric guitar
As a first approximation, acoustic amps are designed and built as if they were small PA systems.
Acoustic amps have nominally flat frequency response in the electronics. Some have special EQ functionality targeted at electroacoustic guitars: Fender's Acoustasonic has a dynamic filter to reduce piezo quack; many acoustic amps have some kind of notch filter to reduce or eliminate feedback due to the resonance of an acoustic guitar's body. All of these tonal modifiers should be (and in my experience, always are) defeatable.
Most acoustic amps of reasonable quality will have a limiter (usually not defeatable) to protect the speakers from overload. Limiter design is a bit of a black art. Part of your audition of an acoustic amp should be to push it to the point where it begins to distort. A well-designed limiter will leave you thinking, "Gee, I can hear some distortion. I should turn down a bit." An amp with a a poorly-designed limiter (or no limiter at all) will make you cringe and say, "What was that awful noise? I never want to hear that again!"
The speakers in an acoustic amp do as well as they can given the restrictions on cabinet size and price point. At the lower end of the market the designers tend to put an inexpensive woofer and tweeter in a cabinet designed to fit all the components and call the result a full-range speaker system. As you go upmarket the designers pay more attention to component selection and design for the speaker system; they'll actually put some effort into designing a speaker system that approaches a reasonably flat response. BTW, any acoustic amp worth its salt will not have an open-back cabinet.
In all cases the low-end frequency response of an acoustic amplifier will be limited by the physics of using a small enclosure and speaker(s). Some designers may attempt to compensate by boosting the low end response in the electronics to compensate for the low-end roll-off of the speaker system. (Actually, I'm not aware of any acoustic amps that do this. It is technically a possibility, though.) Doing this is generally a mistake, as it reduces headroom and available volume.
You don't need lots of low-end for a guitar. Just as long as the low E string sounds balanced with respect to the rest of the instrument, you'll be fine. Don't worry too much about the specs. The way frequency response and power specs are written for these amps, they're entirely meaningless anyhow.
I've tried a lot of different acoustic amps.
My advice would be to avoid all of the Fender products. I've tried most of their Acoustasonic line (original, 30, Ultralight); none of them get anywhere close to having a uniform flat response.
The low-end Ibanez acoustic amps make even the Fenders sound good. They're inexpensive, and a complete waste of money.
An Acoustic Image head paired with a Raezer's Edge cabinet makes an excellent combination if you can afford it. The AI combos (Coda and Corus) look attractive on paper, but haven't sounded good in person.
Some of the Genz Benz acoustic amps sound very good. I played several; the Shenandoah Jr. was my favorite.
I have an AER Compact 60. It's expensive (almost as much as the Acoustic Image products) but it sounds great and has tons of headroom considering its size and weight.
I also have a Phil Jones AAD Cub. I believe that this is the smallest, lightest acoustic amp you'll find at a one-half cubic foot and less than 12 pounds. It's also reasonably priced for an amp of its sound quality. The Cub's low end actually extends further than the AER Compact 60's, but there's slightly less volume available. Still, the Cub has plenty of volume for my solo gigs in small rooms. I've also used the Cub for my stage monitor where there's a house PA.
Finally, considering that an acoustic amp is really just a compact PA, I'll mention the Yamaha STAGEPAS 300. You'll need an active DI box if you want to plug in a guitar. You can run a modeler's outputs straight to the line inputs on the mixer of the STAGEPAS.