I believe security does not play any great difference. Because it is product dependent which is independent of OS.
Beg to differ profoundly. There are great differences in security between OSes, much more than between a server like Tomcat running on one OS vs. running it on a different OS. Security always concerns a complete environment; the most secure server in the world doesn't help if the underlying OS is not secure.
But debugging log and application is cumbersome in Linux when compared to windows.
Not sure what you mean by this. Web apps running in Tomcat are the same everywhere in terms of logging and debugging. Can you elaborate?
I believe size of war file matters because tomcat takes time in reading resources of a war file which is best in Linux than in windows.
That may or may not be the case, but startup time on a production system would be an exceptionally bad criterion to choose an OS, especially if the difference is (at most) between seconds and minutes (and probably much less).