This is a problem: you cannot determine it on the fly. Besides, there are too many different versions of even the major browsers and nearly all of them have some incompatibility. You can find some reference material, but ultimate results can be achieved only through testing. Cross-browser compatibility is a complex and not 100% solvable problem.
I can only give you an advice based on my own opinion: don't try to make your pages look identical on all browsers: it's nearly impossible. Instead, try to devise more fluid and flexible page design the way that the incompatibilities would not look critical. For that purpose, keep it "as simple as possible, but no simpler" (© by A. Einstein, see
http://en.wikiquote.org/wiki/Albert_Einstein[
^],
http://quoteinvestigator.com/2011/05/13/einstein-simple/#more-2363[
^]).
—SA
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