It looks like (in Ghouls 'n Ghosts) the trunk is actually a separate texture to the canopy. So the trunk doesn't have the distort effect, and the distort effect starts at the very bottom of the canopy texture.
Make sure your hotspot is in the right place too. If the sine effect is spinning your tree, maybe your hotspot is in the middle of the tree texture. Place it at the bottom of the trunk (or bottom of the canopy, if you split the trunk and canopy into two different textures) and you should get much better results.
Hand animating does look a heck of a lot better, but it also affects VRAM usage a lot too. I created a 20 frame animation for five different trees, put them into a .CAP, and created a dynamic wind effect to animate them. Looked great! But what would have been 5 different textures using warp/sine/distort effects, became 100 different textures with this hand animated technique. Not cool.