The winner is: With whom am I speaking? You wouldn't say, "The car am I driving in?". And you should avoid dangling prepositions. If your sentence (or clause) ends in a preposition, it is either extraneous, or your sentence requires rewording.
Terminal prepositions are poor Latin , but they are perfectly acceptable English . The prejudice against terminal prepositions (and split infinitives, as well as such abominations as the s in island) came from a period in English linguistics where a bunch of grammarians thought that English wasn't dignified enough, and tried to pretend that it was a Romance language by shoehorning the language into awkward and ungain…
"I passed the man in the red hat by." pass-by
"I threw all of my old, useless papers out." throw-out
To repeat the parent's point: the stricture against ending a sentence with a preposition is simply a bias for grammatical structures that English inherited from Latin (through French) and against structures inherited from German.
The rule against splitting infinitives falls into the same category. It is not possible to split an infinitive in Latin because infinitives aren't made up to two words.
Again, these two rules (and others like them) are about biases, not about grammatical correctness or even clarity of communication. When you say "Who am I speaking with?" and "To boldly go where no man has gone before.", no one is actually left scratching their heads and thinking "I wonder what he means?"