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[T]here are two paths to go down for timing analysis, classic and TimeQuest. Choose up front which way to go. If you only want some basics, like global clock domains, clock-to-out's, and Tsu's, Classic is fast and easy. If you want more in depth, TimeQuest has the power.
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If you are already familiar with the Classic Timing Analyzer and have only simple needs, then it's fine to stick with it for now.
If you aren't particularly experienced with the Classic Timing Analyzer already, then consider using TimeQuest no matter how simple your needs.
Even though "TimeQuest has the power," TimeQuest is easy to use if what you need to do is simple. (It can seem hard for simple things if you are already experienced with the Classic Timing Analyzer, but that's only because TimeQuest is new to you.) If you are learning an analyzer regardless of which one you choose, you might as well use TimeQuest because it will be the one to use for future device families and because it can handle more things that could come up in your designs even in current device families.