It depends. The purpose for the 6.5mm originally was the fact more current was passed through the lines(larger gauge wire), the jack sizes continued to become smaller as the purity of wires became higher as well as certain design flaws were fixed(not twisted, bent or stripped lines) and your were able to pass more current through a smaller wire configurations. now a days jack sizes mean little because the wire gauge size are unchanged from one cable to another. Most people only use a 6.5mm(1/4) plug as an adapter to certain devices that don't have 1/8 jacks.
BUT, in cases when you have fairly large wires for transferring high currents you would want to use a larger jack connection so you are not limiting heat and current transfer. Using a standard 1/8 connector on a line that has a very large load can cause some problems as you don't have a big enough contact area,even if you are using silver/gold plated plugs with large 24awg wired it would be a waste of wires if you are trying to transfer that power through that 1/8 pad. That would just be impeding the flow of current,and that current would be lost as heat dissipation.