Forget your ears! They are the least trustworthy device you have!

At least give them a level playing field... The EXACT same file, when played back even a fraction of a db louder will sound different to your ears. They are very non-linear (and sensitive to volume) organs! In general, up to a point, the 'louder sounds better' rule applies.

Now, I don't know if you have thought about this, but feeding your arranger's output, summed into mono internally, and run through ONE cord may have a slightly different level to BOTH channels run in stereo to TWO channels on the board. So, before you make any hard and fast rules about whether internal mono sounds 'better' or 'worse' than externally summed mono, make sure you are monitoring the sound level at EXACTLY the same volume...

And I am afraid that most PA's don't have sensitive enough meters to tell you you are IDENTICAL on both systems. You might have to stick up a mike in front of the speaker and run into a DAW with some highly sensitive metering plug-in to be sure (and test levels with a sine tone or something non varying)...

Doesn't sound like a lot of fun, does it? But before you can well and truly say for SURE there really IS a difference, it needs to be done.