"Who would win in a Thanos vs. Darkseid fight?" is a question as old as the characters themselves. One is the Mad Titan, capable of taking down the Avengers with relative ease, the other is the Lord of Apokolips, sitting at the absolute mountaintop of DC villains.
Darkseid and Thanos stand as the ultimate villains of their respective universes, and for good reason. At their peaks, both would have the universe in the palm of their hands. Thanos, when he has assembled all the Infinity Stones, has the power to virtually do anything he wishes (in the comics, traditionally to woo Death). Darkseid also has a universe bending weapon of his own. When equipped with the Anti-Life Equation, reality itself kneels before Darkseid. Given such powerful concepts, most of Darkseid and Thanos appearances feature them in search of their ultimate power.
The connections go beyond just being gigantic foes for their respective universe's heroes. Darkseid was created in 1971 by comics legend Jack Kirby and directly influenced Jim Starlin in designing Thanos two years later. While that linked origin is the source of debate, most fan conversation centers on who is the most powerful. However, the answer is quite simple: Darkseid.
Even if the two villains fought at the absolute peak of their powers, with Thanos armed wielding all the Infinity Stones and Darkseid possessing the Anti-Life Equation, there is a clear winner. Thanos would still have to snap his fingers; for Darkseid, the battle wouldn't even have to begin before it was over, given the mind-wiping nature of the Anti-Life Equation.
To have a truly fair fight between the two, Darkseid and Thanos would have to face off without their respective reality changing weapons. Here, things initially appear more level. Thanos is often at the center of a fight and has routinely taken down the best Marvel has had to offer him; in the comics has battled against the likes Silver Surfer, Beta Ray Bill, Thor, and even held his own against Galactus (while he eventually lost the fight against the World-Eater, even getting a solid hit in is a feat worth mentioning). But while Thanos has resources, Darkseid is arguably the most resourceful person in the Galaxy. The Justice League are inherently more powerful than the Avengers but, even then, it is little more than a chore for Darkseid to take them down. Most can not survive a blast from his Omega Beam; even Superman, the peak of all superheroes DC or Marvel, is brought to near-death by it.
Darkseid brings fear to the entire DC Universe, heroes and villains alike tremble at the mere mention of the Apokoliptic Ruler, and for good reason. Darkseid has something Thanos does not: centuries more experience. Darkseid has been in near-constant war with literal New Gods for centuries, his battle senses and tactics perfected to the point where he barely ever flexes his true muscles. The few times he ever lost in battle to anyone was under extremely specific situations, almost flukes in the larger scheme of things. Thanos is indeed formidable and without their universe ending weapons, the two would naturally have an incredible battle. Eventually, though, Darksied's pure strength, infinite resources, auto-win Omega beams and a vast amount of battle experience would give him the ultimate edge. Simply put, Darkseid wins because Darkseid is.
The debate of Darkseid vs. Thanos has become so heated that it started to trend on Twitter. Unsurprisingly, Darkseid has been winning with 66% of votes at the time of writing from a pool of 30,000 at the time of writing.