They do not have the same meaning. Both are grammatically correct: “to do” and “doing” are forms of the verb—infinitive and participle, respectively—being used as nouns. We do this all the time: I like to read, I like reading.
And both expressions as written trigger a sense that “we just wouldn’t say it that way,” meaning that they’re not what we generally see as idiomatic American English. We typically don’t use “desire” as a verb much any more. And we generally say “I’m interested in” rather than “It is interesting to me.” But neither form is incorrect.
If I were in an old British movie, I might well tell the hotel desk clerk, “I desire a room.” And if I wanted to keep the object of my curiosity a bit at arm’s length, I might well say “Watching a Venus flytrap process its food is interesting to me,” but not “I’m interested in watching carnivorous plants devour insects.”
But the real difference is in the word choices themselves: “desire” is a much stronger expression than “interest,” although they might be seen on the same continuum. One’s interest might never reach the peak of desire, and one’s desire might never weaken to the level of mere interest. They might also be so far separated in shades of meaning that you would never use one in place of the other; that depends on context.
So it comes down to meaning, not structure.
Neither sentence is in the passive voice.