I personally prefer six-degree tapers for a number of reasons. Shallower tapers make a stronger joint. 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. There is less difference between the smallest and largest diameters of the tenon. So when the seat changes thickness with changes in moisture content, there will be less of a tendency for the mortise to pull away from the sides of the tenon. However, all this can be taken too far.
During assembly, shallower tapers are more likely to split a seat 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. When using hand tools, it is more difficult to bore a hole at the correct angle than to drill an approximate hole and ream it perfect. However, one oft-mentioned advantage of tapered joints does not hold water. I don’t agree that tapered joints get tighter from the weight of the sitter. 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. When there is less wood to remove from the mortise, 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 aesthetic 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. Factors other than which taper is used (whether the tenons are kiln dried, for instance) probably have more effect on the joint’s strength.