Do you want this or that?
That is, “Which do you want—this or that?”

I want this or that.
(In other words, I'll take either choice—they're both OK.)

Do you want this or that?
That is, “Is it true that you want either this or that?”

I prefer water to alcohol

I can go there with you, but I prefer to travel leisurely.

There's nobody I'd rather commune with under the Tree of Voices.