I'll go with Thanos. I can't see Thanos being dominated by anyone short of a cosmic entity and maybe not even then. He was powerful enough to shut the Maker's mind down (the Beyonder in a female body) and mentally enslaved the Fallen One (Galactus's first herald).
Of course, if Strange could pull off the stunt he did against Galactus, about causing him to feel the deaths of everyone he killed, he might win. I'm not really sure if this would count as a "mind battle" though.
As a Titanian-Eternal, Thanos was destined to be powerful by nature. Most Eternals have some level of Superhuman strength, and the ability to manipulate cosmic energy for attack or defense. Thanos, however, was a mutant, and was born with even more potential than the average Eternal. Thanos further augmented himself after his banishment from Titan using both mystic and scientific means, increasing his already formidable might to nearly incalculable levels. Through meditation he honed and increased his latent telepathic powers, becoming a formidable psionic opponent. He also sharpened his energy manipulation abilities to great effect, even deveoping the ability to disrupt/manipulate matter.
His powers were again increased by Death when she returned him to life, giving him the might to fight such powerful beings as Tyrant, and Odin (King of Norse Gods) on nearly even ground. His body is tremendously resistant to injury, can go without food, water and even air for an indefinate period. His body is also able to withstand a total vaccum (such as in deep space), and is incredibly strong. His exact strength level is unknown, but it seems he might be as strong as or stronger than such heroes as the Hulk or Thor. His abilities to manipulate cosmic energy have been increased to a staggering degree, and he can utilize it to grant himself near-invulnerability, or to project the energy from his eyes or hands in the form of light, heat or concussive force.
However, what makes Thanos truly dangerous is his high-degrees of intelligece, cunning, and razor-sharp logic. He possesses not only the Advanced knowledge of the Titans, but also technology and skills gained from all over the Universe. He is obsessed with knowledge, as he believes that knowledge is power. Thanos is also a hightly skillled combatant, having trained himself in many different fighting-styles from throughout the universe.
Strange is underrated, Thanos is (a bit) overrated.
The reason why Strange is underrated, is because he's a good guy, and doesn't like violence. The reason why Thanos is overrated, is because he looks and acts cool.
Strange wins. He has faced a lot of cosmic beings without hiding behind alien advanced technology or the "I can't die"-stuff.