Which is best, using balanced or non-balanced connection?

Thanks to all for your inputs. They were greatly appreciated. I'm to go with balanced.

Thanks again,

Marvus

"Thanks to all for your inputs" Lol, very punny!

All my gear is balanced. Your challenge will be to find a decent turntable with balanced outputs or decent rca to XLR signal converters or adapters if your pteamp only has XLR ins and outs. Very few good turntables have XLR outs. This of course assumes that you spin vinyl. If not then no worries!

I have a preamp on my desk and an amp on the shelf above it.  The cable runs amongst various other signal and power cables and there was always an audible level of hum coming from the speakers.  Substituting RCA for XLR removed the hum completely.  So there's that.  In less challenging situations, though, I don't think either has an advantage.

Along these same lines (pun intended) I run RCAs from my table to a phono preamp and balanced from the phono pre to the pre, then RCAs to the amp that does not have an XLR connection.  Is there any point in running a balanced interconnect in a circuit that begins and ends with RCA?  Would it make more sense to run a high quality RCA from the phono pre to the pre and use the single XLR input on the pre for my DAC that has an XLR out?  Now that I've posed the question I guess I'll go to the trouble to give it a try, but I would be interested in hearing about your experiences with similar situations. 

Which is better?

Yes.