Yes, rewards go up with difficulty. See here. Crowns on Normal are 33% less than crowns on Elite. Crowns on Advanced are 16% less than crowns on Elite.
From 2011/04 to 2013/07, there was only one difficulty level, which we now call Advanced. This is the difficulty, on which the game was designed to be played. Arguably Advanced should be called "Regular", Normal should be called "Easy", and Elite should be called "Difficult".
My recommendation is that you play on Elite, until you start spending Sparks of Life. Then play on Advanced, until you start spending Sparks of Life. Then play on Normal. Then try Elite again. Basically, play on the most difficult setting that doesn't frustrate you. Cheers.