As per my understanding, most of the Gyros in big jets are electric driven but I am not sure if the smaller planes also have the electric driven or vacuum/pressure driven Gyros?
Yes small planes have electric gyros as well. It can be as sophisticated as Garmin 1000 in Cessna 172 or Russian made electric artificial horizon gyro powered by accumulator in a glider Blanik L13. I heard battery didn't last very long though:) Also all turn rate indicators have gyros and the ones I saw were electric powered. This ensures that you can still survive if a vacuum pump fails. Turn indicators used in the eastern block made gliders are powered by simple 4.5V battery.
Many planes are being/have been retrofitted with glass panels that use attitude heading reference system (AHRS) in place of vacuum driven gyros, with 4-hour or more battery backup in case the plane's electric system goes down. Examples are the Garmin 1000 as mentioned, to something smaller like a pair of G5s or a G500. https://buy.garmin.com/en-US/US/p/pn/K10-00280-00 https://buy.garmin.com/en-US/US/p/pn/TXi-0G500-03 https://buy.garmin.com/en-US/US/p/pn/010-G1000-00