Nope, they use even more powerful forms of power generation. They can do things like that in fiction.
The only Federation advantage is the ability to create sparkly glowly things with their technology. That’s really about it. Their weapons are far less powerful - photon torpedoes, according to the tech manual, carry 1.5 kilograms of matter and 1.5 kilograms of antimatter as reactant, giving them a high-end yield of 64 megatons. Heavy turbolasers, the large turrets on the dorsal, have, based on calculations derived from the asteroid vaporization scenes in TESB, have long been estimated to have the ability to dish out blasts measuring in the dozens to hundreds of gigatons, low-end. More recently, according to the recent AOTC ICS (Incredible Cross-Sections), this figure has been given a more solid figure of 200 gigatons, at least, for an older ship of less than half the size of a Star Destroyer.
What’s more, the same book puts large ship shield strengths for the Empire in the teraton range. Some calcs for ISD’s go around 40 teratons. This essentially means that you’d need well over a thousand Federation ships all firing simultaneously at each Imperial ship in order to have a chance against it.
FURTHERMORE, the Empire vastly outnumbers the Federation… whereas current estimates put the peak of Federation fleet numbers into the 8,000-12,000 range, the Empire had, at its height, 25,000 Imperial Star Destroyers alone… this doesn’t even include smaller ships such as frigates, dreadnaughts, cruisers, corvettes, gunships, or the like.
Speed: It was going to take Voyager, a top-of-the-line hotshot ship with the best warp speeds around, 75 years (ignoring technobabble solutions) to cross 70,000 lightyears. Conversely, an Imperial ship can do that distance in a matter of days (as seen in AOTC and TPM, where starships travelled from Core worlds to the Outer Rim in a few hours… “days” is a conservative estimate). This essentially means that Imperial ships can strike anywhere in the Alpha Quadrant, without warning, with impunity.
To put things simply: A dozen Imperial Star Destroyers can destroy all the major worlds of the Federation inside a week.