Solid copper or stranded copper for speaker cables? What is your choice and why?

If you want the sonic benefits described by @elliottbnewcombjr (resulting from cables made from multiple strands of individually insulated, solid core wires) then you can either braid CAT wire or check out offerings by Harmonic Technology such as one of the variations of their Pro9 or Pro11 speaker cables (made from OCC). Either option should sound good.

I went with OCC cables from RAMM Audio. I really like the topology of these cables. Six individual conductors each with six OCC wires. Great shielding, A bit of a hassle to deal with all those wires when connecting to the terminals but well worth the effort. And being DIY, the cost was reasonable. 

@lanx0003 

As some has suggested, listening at home is the ultimate test.  Just keep in mind that if you have an old version of a cable, it not necessarily a valid representation of current offerings by that manufacturer.  See what's new, and give it a listen.  

I have Morrow Audio speaker cables which are multiple strands and the ones I have are 1500 strands per cable. 

Stranded.

Having worked in a metrology lab for an aerospace bearing manufacturer, an R&D department for a major gas &oil company, and in gas & oil operations with electronic controls and monitors protecting millions of dollars worth of equipment, if it's good enough for that duty, it's good enough for my stereo.

Belden, Canare, or other high quality cable.

FWIW, in industrial applications we almost never use solid conductor wire.  They have a tendency to fatigue and break at junctions.  Especially if your wire strippers put a good nick in the wire when you are working with it.  Thermocouples being an exception, but those have been replaced by thermistors and RTDs, for the most part.