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

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.

"Balanced rejects noise that why all professional audio gear is balanced. So doesn't matter on short cables, but anything longer than 6ft should be balanced ideally. I run 12 ft cables, all XLR."

Over 99% of all pro gear isn't balanced. Pro audio typically uses point to point balancing. The components themselves are single ended and the signal gets converted at the inputs and outputs. In order for the component itself to be balanced, all the parts in the signal path have to be doubled up to make a path for the 2nd signal conductor. To do it right raises the cost of the component significantly. Doing point to point allows for longer cable runs and better noise rejection, so its a good thing to do. However, if you want better sound quality that balanced operation delivers, the components themselves need to be balanced.  

052rc

In order for the component itself to be balanced, all the parts in the signal path have to be doubled up to make a path for the 2nd signal conductor.

That is false and it’s amazing how frequently this myth is repeated. Many truly balanced components use differential circuits and that is not at all how they work.

However, my question is how I should connect the external amp for the best sound. Should I use the balanced or unbalanced connection?

@mjrice2 If your amp has a balanced input and is internally balanced, driving it balanced will allow it to have slightly lower distortion.

If the equipment supports AES48 you'll get less interaction (possibly quite a lot less) with the interconnect cables. In my system even though its quite revealing, you can't hear interconnect cable differences on this account.