Galactic Empire outmatches New Republic because of size predominantly. However, the tech of New Republic is better, the starships are of a higher, better level. New Class Modernization Program was an entire campaign designed to completely upgrade the Defense Force. While I don't think giant tons of starfighters costing literally 1 000 000 000 000 of credits were turned to scrap, and rather, they just added in the new ships to the existing force while sending the oldest ones to more menial duties, there were many years after the program's commission, so the replacements were probably pretty massive, and the fleet was simply of a higher technical level.
However, New Republic leadership by 25 ABY was quite possibly the worst ever. Government was weak, corrupted, incompetent. While they followed the democracy and live was all good, the quality of leadership to deal with the invasion was the worst you could imagine. Coordination of cross-planetary defenses was null. Communication was terrible. Nothing bad in a peaceful time, all the planets actually obviously prefer to live on their own, but in the face of invasion the massive incompetency was a disaster. Galactic Empire was enormously controlled, tight and coordinated and operated coherently on a galactic scale with full coordination. The comparison is insane.
Then you have to remember that New Republic is the result of the giant war between Rebel Alliance and the Empire. While Palpatine's death resulted in the regional Moffs defending their own areas, and the Rebel Alliance just going star-system after star-system beating the Empire, it was still huge. Losses were immense. Then you have the Yevetha, Thrawn, Second Imperium etc. - and these wars were a threat of that scale only because of how shattered the galaxy was. It was a fresh rebuild. New Republic never had the time to build a force even slightly as large as that of the Empire.
The tech advantage of NR won't make the cut, when you just have 1/3 of the fleet of GE. Especially with terrible leadership.
Krayt's Empire is another story. The tech difference is many, many times larger, and it was built directly off Fel's Empire, which had dozens of years to build its strengths. As far as leadership and size goes, GE is still probably easily superior, but tech differences make up for it. Having dozens of trained superhuman Sith Lords with Force precog and an ability to infiltrate anything anywhere helps too.