I personally prefer six degree tapers for a number of reasons. Shallower tapers make a stronger joint because when the joint is driven home it locks tighter, and takes more force to remove, than a similarly sized joint of a steeper taper. Shallower tapers should also theoretically be stronger because the difference between the smallest and largest diameters of the tenon is less; when the seat changes thickness with changes in moisture content the mortice will try to pull away less from the sides of the tenon. All this can be taken too far as shallower tapers are more likely to split a seat during assembly than steeper ones.

Taking this to the extreme, why not use cylindrical tenons like those on the stretchers and spindles? Assembly is easier with tapered joints and the tighter the stretcher joints in the undercarriage the more this will be noticeable. When using hand tools, it is harder to bore a hole at the correct angle then to drill an approximate hole and then ream it perfect. Tapered joints don't squeegee glue off the joint the way cylindrical ones do, thought admittedly this is a minor issue. However, one oft mentioned advantage of tapered joints in my opinion does not hold water; that tapered joints get tighter from the weight of the sitter. A joint is allowed get tighter only when that joint fails and our goal should be to make a joint that will not fail because it is tight to begin with.

Aside from issues of strength, six degree tapers are easier to use than eleven degree tapers for several reasons. Less wood to remove from the mortice means the reaming process goes faster. Also, the reamer is less likely to get started at a drastically incorrect angle because narrower tapers have more bearing surface on the cylindrical hole.

On an aesthetical note, I find that six degree tapers allow me to slim down the turnings where they enter the seat making them visually lighter. However, eleven degree tapers tend to be smaller where they come through the seat making the joint less obtrusive.

Admittedly the difference between one taper and another seems a trifling matter and other factors (wether the tenons are kiln dried, for instance) probably have more effect on the joint's strength than which taper is used.