First up is The Stick. It is about 1.5 feet long in the version that I've been using and kind of reminds me of a plastic rolling pin with the center part sectioned off like beads so that they can roll independently.
I like that I can roll out my muscles while lying down sitting, or perhaps even standing. It is just like rolling out dough. A moderate press is all you need to feel an effect. Go too hard and you'll just be hurting yourself. Sometimes, there is a chance that your skin can get a little pinched in between the sections. I also doesn't work too well right up against bone (i.e., the shin), but otherwise, my quads and hamstrings and calves love it after a good run!
Next up is the foam roller.
It is a styrofoam-type material and comes in different "densities" (imagine a light/porous styrofoam ball vs. a tightly-packed styrofoam box). This baby comes in various lengths, but I typically use a 3 ft one.
There are a variety of foam roller techniques to get a good roll-down, since you have to be on the floor, so this is a disadvantage. You need to be careful how much of your body weight you place while rolling out various parts of your leg, lest you over-press your muscles! And yes, you'll likely be on all-fours or something awkward like that as you try to shift your weight correctly.
However, I think using your body weight as you have to with the foam roller creates a much deeper massage than The Stick, and sometimes, you really do need that level of pressure.
All in all, I think both of these devices have a purpose and place in general muscle-relaxation for runners. If I had to purchase one myself, I would get The Stick beccause it is smaller, more compact, and easier to use. But I would definitely miss the foam roller if I no longer have access to one...