I would recommend that you differentiate your titles from your competition. Google has said that they value "diversity" in the SERPs. I rarely see two pages with the same title appear for the same query.
I wouldn't copy titles from a competitor. If a competitor has copied your titles, you might want to think about changing a word or two in yours. Especially think about changing words near the end of the title where there is less ranking effect and more ad copy effect.
My main competitor is constantly duplicating everything I do - keywords, content topics, links, etc. And, it drives me crazy but gives me the motivation to work smarter than him to continue to out rank him on all of our targeted keywords... to build a higher quality site!
I have a client that has a competitor that's been copying his content/articles/press releases/titles and everything else he can get his hands on and doing this for years, in spite of getting several websites removed due to copying copyrighted data, and another take down via a Google DMCA and having multiple copied press releases removed.
I constantly urged my client to just stick to Google rules and keep adding content and that competitor will bite the dust some day.
Recently my client went up in ranking for his major keywords and also had a rise to Pr 5 the other day and this competitor is still at Pr 4 and has dropped in rank for major keywords in last several months and now he's having a big sale on his site.