How can you tell that a Christian is full of pride?

Tell him that you think this is the case.

If he is offended, or enraged, or points out your own failings, your diagnosis was probably correct. 

If he agrees with you, and says he wishes he was a humbler man, you were probably wrong. 

Reprove not a scorner, lest he hate thee: rebuke a wise man, and he will love thee. Proverbs 9:8