Galactic Empire (RotJ) vs. Dark Empire (DE)
The Galactic Empire in Legends as of RotJ
vs.
Palpatine's Dark Empire as of, well, Dark Empire
The two different timestamps of the galaxy are merged via a usable wormhole in each one's outer rim.
No interference by outside forces.
Round 1: No Force storms
Round 2: all bets are off
Who wins?
The Dark Empire wins. The Galaxy Gun can one-shot anything from anywhere in the galaxy, the World Devastators are essentially Star Forges that produce an endless quantity of ships, the Eclipse-class SSD's rival the Death Stars in terms of destructive potency, and apparently they also have the larger fleet:
The Emperor's death brought little respite to the people of Byss. Within months, the Emperor inhabited his clone body and began the rebuilding process. For years, Palpatine simply focused on building up his own power and preparing to strike at the New Republic. The shipyards of Byss worked day and night producing massive battlestations such as the Galaxy Gun and vast warships like the_Eclipse-class and Sovereign-class Star Destroyers. Around the planet Byss, a marshaling of military forces took place unlike any previously seen in the history of the galaxy. The renewed war against the New Republic was short but devastating.
Byss and the Deep Core
Plus, the Emperor himself is far more powerful as of this time period, and could most likely just kill his previous incarnation, or at least distract him enough to break his domination of the Imperial Military, which would render all of the Galactic Empire's fighting forces ineffective. The Dark Empire would just cut a swath through the galaxy virtually unopposed.