Compare the execution plans. Since the queries take so long to run, begin with the estimated execution plan. They will highlight differences between the two servers - say an index exists on one server but not the other. If you're not comfortable with interpreting execution plans, then post them here as .sqlplan attachments.
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Understanding and using APPLY, (I) and (II) Paul White
Hidden RBAR: Triangular Joins / The "Numbers" or "Tally" Table: What it is and how it replaces a loop Jeff Moden