Parameter sniffing is likely to affect your query. Goggle it and look for articles by known folks - I think Gail has one of the best articles.
More importantly, there are a quite a few index scans without predicates which suggests that there's scope for adjusting your indexing in favour of this query. I think this is your best shot.
You may well discover that with tuned indexes, using OR will outperform UNION in this case - don't forget to test it.
For fast, accurate and documented assistance in answering your questions, please read this article.
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