Walk: JCCSF, Mindful Body
Distance: 3 miles, Pilates mat class, teach yoga class
Turns out my fitness center (JCC) offers some Pilates mat classes which are very highly regarded in the Pilates teaching community. And very highly regarded by me because they come with the membership (as opposed to the machine private and group classes which range from $28 to $85 even for members). As you might have learned from ciwt, I believe in exercise of some sort for everyone as often as possible, so I don't favor very expensive forms and do favor things like walking.
Anyway, the Pilates mat class was excellent. It is almost as if Joseph Pilates did a study (or probably in fact he did) and figured out all the muscle groups that either aren't used in yoga or are used in different ways. AND vice versa. There are many ways yoga uses and opens the body which aren't addressed at all in Pilates.
Specifically Pilates zeroes in on the abdominal core (which actually includes the quads, the abs, the lower back, the hamstrings and even the arms and shoulders). Judging from what I felt today, if you think of the central core of your body from your neck to your ankles, this is the core Pilates isolates and works in a very aligned (straight) way. Yoga involves, for a few examples, more fluid overall body movement/opening, more coordination, more stamina if you will, more breathwork, self-awareness/connection with a capital S.
The two disciplines are very different and complementary. I'd say if you can (and are interested) yoga and Pilates are the Perfect combination. And if you're interested in adding Pilates, maybe spend the money on a private Pilates lesson or two and maybe a Pilates group with machines, then, if you want to do it on a regular basis and there's a gym offering Pilates mat, join it and take the mat classes as part of your membership. The privates and working with the machines will absolutely line you up and your body will learn where the work is going. Then you can do the mat work with that knowledge.
OK, I will say, if you can only do one, yoga is the one I would choose. It's more complete, involves movement and you can add Pilates principles and alignment to the yoga practice. Or you can do some/15+ minutes ab and arm weight work on your own before or after or on yoga days off. Because it is so absolutely straight there's really isn't a fluid way you can add Pilates to yoga - except to stop doing Pilates and begin doing some yoga.
On the other hand, if you are aiming for the most beautiful abs in the world, choose Pilates. And if you're okay with the expense, work with a private instructor or small machine group. Every once in a while I see a Pilates instructor walking down the street in one of those tee shirts that stops above the midriff and WOW!!