Surely both versions are about "how" the speaker feels:

Cada vez que veo esa película siento escalofríos. - Every time I see that movie it gives me the shivers. (lit: I feel the shivers)

versus: Rafael se siente mareado. ¡Trae un vaso de agua! - -Rafael is feeling dizzy. Bring a glass of water!
There must be a better way to determine which version to use, no?

Or is it that with sentir it's when an external force is affecting the speaker and with sentirse it's a matter of personal, internal sensation/emotion. It seems to be a very fine line of definition . . .