I could write a book about right here on this topic but don't have time.
Balanced versus unbalanced can have three big differences. Impedances, level and grounding...along with the wiring.
Balanced means the same signal is run inverted in phase on a second line. That means when one side is going up in amplitude, the opposite phase is going down equally. Equal amplitude going in opposite direction means double the voltage (compared to unbal) over any noise...BIG advantage. Also means 6db more signal, stated differently. Nothing automatically means it can't also be a -10db signal. It's just a loose standard in audio that balanced is run at +4. The voltage on the line between -10 and in a balanced +4 is much larger than looking at those two numbers makes it seem.
Interfacing balanced driving unbalanced...versus unbalanced driving balanced has different issues and it gets glossed over all the time. Buying an adapter without understanding the issues than can arise, including damage is common! The main thing to remember is to NOT short any driven output (unless it's a "servo" balanced one). Unbalanced driving a balanced input has less dire possible results. The adapters can get you there normally. Balanced outputs going to a unbalanced input require more care to get right when you're not familiar with all the tricks and pitfalls.
A high quality (expensive) transformer is still the best way to interface. The mention I saw of the Rane transformer having a noise issue suggests miswiring as they are pretty good ones in those. Like many things in audio, the transformers that are good were largely done away with due to expense, size and weight and when they're quality, they exceed in use the theorical numbers of op-amps...this is contrary to convential thinking of today. I've never heard an active matching box that didn't hurt quality much more than I'm willing to accept.
Gary, if one device was wired with a different pin as high, that makes no real difference as long as L and R are wired the same way. All it does is flip absolute phase which has about as much chance of winding up being right as wrong. That's referring to the "Wood Effect". Absolute phase is irrelevant with most modern music...except the type of stuff I put on the CF disc for the most part!
Broadcast standard in the field was at one time pin 3 high and what I call semi-pro audio used pin 2 high. More correctly I think, Europe used pin 2 and eventually that became more typical. So devices that are around with pin 3 high are just stupid people...it's just they were using a "different standard". Means little in my field except always looking at the manual for the gear when wiring it.