Which team has the best record, yours or theirs?

The underlined portion is fine, except for the use of the word "best".  

The sentence presents  a comparison between two teams: yours and theirs. The original sentence uses "the best", which is a superlative, typically used when comparing more than two items. However, since we are comparing only two teams, the correct form should be a comparative — i.e., "better" rather than "best."

So options A and B are anyways eliminated. In case of option C, "Which one team..." sounds redundant — “which” already implies a singular choice, so “one team” is awkward.

The correct choice is option D.