Both Thanos and Darkseid are craggy faced, megalomaniac outer space bad guys who are intergalactic menaces. The two characters are compared often, and to me, it's not even a contest: Thanos, the "Mad God," is the more frightening, the more intimidating, the more fearsome, the more complex, the more intriguing, and is featured in way better stories. And it doesn't surprise me in the least Thanos would make it to the big screen ahead of Darkseid.
Thanos has a more interesting motivation and origin.
Thanos is a nihilist in love with Death herself, who wants to give her the universe. Darkseid, on the other hand, wants to solve a math problem.
Beyond that, Thanos has a far more interesting psychology at work. He's terrifying for a reason Darkseid isn't. Darkseid is an authoritarian dictator who wants control. Thanos, on the other hand, has a cold, crystalline commitment to nihilism and death terrifying to any rational being. He commits genocide because he is philosophically opposed to life: he views it as a disease in a dead universe. He kills because death is beautiful, and life isn't worth living. Thanos tears out grass because its life is hideous to him; the ground would be more beautiful dead and cold. He wants to destroy life on Earth and other planets because our world is far worse off than quiet, crystalline, barren worlds like Mars, Mercury, and the Moon. Thanos proved his commitment to this idea in a cold, personal way: he killed his own mother.
In short, Thanos is terrifying because of the way he thinks, not just because he can shoot scary eye lasers.
There's also an element of pathos in Thanos's motivation, too: no matter what he does to honor Death, she doesn't give him the time of day. Thus far, Death has never even spoken to him. No matter how many successes he has or how many triumphs he has. Even when Thanos tried to get over Death and form his own evil Pantheon of Gods in Avengers: Celestial Quest, you could tell he hadn't gotten over her and his behavior was upping the ante overcompensation.
Thanos has a sense of humor and dry wit.
Voltaire said, "God is a comedian playing to an audience too afraid to laugh." Thanos is very much the same way: one of the most amusing things about the character is how his dry humor is wasted on people terrified of him.
For instance, remember in the Avengers movie when, after being told the Avengers "court death," he gave a wry, dark smile? Is it even conceivable for Darkseid to appreciate wit or wordplay like that?
"You're the Mad Titan. You bring death, pain, and destruction wherever you go."
"I see my reputation precedes me."
Thanos even got off a bit of sly mockery there due to his respect for his enemy, Captain Marvel.
Oh, that reminds me of the next point:
Thanos had respect for his greatest enemies.
Even Doctor Doom, for all his nobility, thinks of Reed Richards as a less talented clown.
Thanos, on the other hand, appeared to Captain Marvel as he was dying from cancer to actually HELP him accept the inevitable, feel no fear, and pass into another world. He even showed up in Captain Marvel's mind to fight him, simply because he felt someone like Captain Marvel, dying of cancer, deserved to go down fighting. This wasn't some evil plan of his; Thanos showed up to ease Mar-Vell into dying at peace because he wanted to help.
So great was Thanos's respect for Captain Marvel, he was horrified to see Quasar become Mar-Vell's replacement and pretender, and beat him pretty brutally for it.
Likewise, Thanos helped his other great enemy, Adam Warlock in the Infinity Watch against the power of the Magus.
Thanos actually came much closer to winning.
All this was not only in-continuity, but in some of Marvel's most important stories.
Thanos is more terrifying and intimidating.
Perhaps because Thanos has a way higher success rate (and again, an origin that doesn't involve solving an evil math problem), Marvel treats Thanos the way Doctor Who treats the Daleks: they only come out when they aren't messing around. Thanos is never used gratuitously, and certainly isn't overused, something that can be said about Darkseid.
Perhaps because Thanos has a much more lively psychology than Darkseid, it's interesting to note it's implied part of the reason Thanos lost was because of his own inner doubt; he's uncomfortable with totally winning. In short, nobody really beats Thanos except Thanos.
Thanos is always drawn dynamically. Darkseid is always sitting in a chair.
There's a tumblr that's nothing but images of Darkseid chillaxing on a couch.
Why is that even a thing at all? I'm going to get into trouble for saying this, but it's absolutely true: Jack Kirby's art got lazier the instant he stopped working with a plotter. If you don't believe me, count the panels for yourself: the average issue of Fantastic Four had 33% more panels than the average Fourth World comic. Kirby's splash pages went from pop out action sequences, like in Fantastic Four:
...to scenes of people just chilling in rooms.
Thanos's poses, on the other hand, suggested confidence, megalomania, and arrogance. And Thanos certainly never stands around with his hands behind his back looking bored.
In the end, this crucial difference seems to summarize the distinction between the two characters. Thanos is a dynamic character with a vivid inner life and Darkseid does the same thing over and over. As a result of lessons he learned in battle with Akhenaten in Marvel's The End, Thanos found conquest and destruction inherently futile, a realization that's been with the character ever since, for example.
When asked who is more interesting, it's no contest.