thanos could win both scenarios, the prep one with sufficient and deft application of deceit and cunning. the straight-up confrontation with greater personal powers and immense speed.
Strange's presence in the DC universe would inevitably attract a lot of unwanted attention from demons, mages and other magical entities. Thanos, being the consummate pragmatist, would simply arrange for Fate or someone of that ilk to absorb Strange's powers for themselves, in exchange for help with getting back to the Marvel Universe. or maybe a map to the Source Wall (where Thanos could study the phenomena close up and maybe find some way of tapping into the ultimate powers it obscures?).