going to ramble, you've been warned...
It's hard to beat chemical energy for energy density so trying to cycle the action with a power source other than propellant gas pressure is going to, in most cases, be bigger, heavier and less efficient than scavenging some of the energy from the propellant gases to cycle. The only successfully electrically powered weapon system I can think of is the mini-gun and some of it larger brothers (the biggest ones like the GAU-8 are hydraulically powered). But in the case of man portable the micro mini-guns are the close we have come to a electromechanically powered small arms.
But electronic ignition on the other hand has huge potentials in small arms if the market would not be so stubbornly resistance to change (as many of the comments here clearly illustrate). Electronic firing is common in anything 20mm and above. Most of those cartridges use electrically ignited primers (though some of them have a mechanical backup, primer that can be electrically or mechanically ignited).
In a bolt gun the big advantage is you no longer have the sear/striker engagement pushing up on the back end of the bolt. Without that moderate force pushing up on that lever (bolt body) it would be easier to get a bolt lockup that is perfectly square and symmetric to the breach/chamber for squeezing the last bit of accuracy out of things.
With electrically primed cartridges the trigger is no long mechanically tied to the guns fire-control so the trigger can move positions, change shape, and have a variety of tactile feels and these changes could be as radically as you wanted to try (again US gun owners are unfortunately highly resistant to change hence the Remington EtronX rifles being nearly indistinguishable from the regular 700). Think about the possibilities for increased accuracy if we can move the trigger where is make the most ergonomic sense not because the action forces it to be there. Think about changes to configurations moving the action around without worrying about the trigger placement.
Bullpups could have equally good triggers!
The ability to interface with an assistive fire control aiming system like Track-Point with no mechanical lock time and no mechanical actuator to release the hammer/striker.
In a semi-auto pistol think about what could change if you no longer need a mechanical trigger bar that needs to get by the magazine to the sear. A double feed pistol magazine becomes much easier. No striker or hammer behind the breach face would allow red-dots to be buried in that volume taken up by traditional fire controls.
A revolver with no hammer spring to fight in double action! Old school meets new school.
In belt feed guns electically primed would be huge, the rate of fire could be tied to pressure on the trigger. Light pressure could create a slower suppressive fire-rate and when a target is actually seen heavier pressure could increase the rate of fire to increase the likelihood of a hit. You could even integrate an IMU (inertial measurement unit, ie accelerometers and gyros) and could use feedback from the sensors and user to adjust the rate of fire to help the user keep the muzzle from climbing while firing again increasing the probability of hits.
Think how much simpler many firearms get when you eliminate all the mechanism tied to the mechanical fire-control and replace it with a single electrical contact (ground through the barrel/receiver) and a switch (trigger) and a small pack of electronics/battery that can be as small as 700 trigger pack or a drop in AR trigger.
Think of the nightmare for the ATF when the difference between an eclectically primed semi-auto and full-auto would become a software change.
Electrically primed ammo could dramatically change the firearms market if the firearms market wanted it. Unfortunately they do not. Remington EtronX primers are still made for the few guys still reloading for it but mostly they live on on some less lethal weapons systems used by the military and police.
-rambling complete, for now...