Apart from the Reshape filter and a few standalone shareware programs, this is pretty much your only option to get decent morphing inside After Effects as well as other programs like combustion* or Fusion. Using masks and a special odd/even stacking order, you can define source and target shapes and areas. You can further refine the alignment by animating the masks over time to acommodate changes in the footage.

• Morph – basic morph to transition from one still frame to another when the source and target are stationary
• Motion Morph – An advanced morph that will also detect the motion of your object and figure it in. A good example would for instance be a bird that flies across the screen and then transitions into a horse running on a meadow.
• Warp – "pull" pixels into a certain direction. Could be used e.g. to get rid of strong lens distortions by tracing curved edges in the footage and aligning them to straight target masks.