Is there a photoshop filter that limits colors, but better than posterize?

You can Save for Web and devices... and then select PNG-8 format, turn dither to 0% and reduce the number of colours down to just a few. I got reasonable results with your sample image by reducing the number of colours to 6.

Try to convert the image to a vector format. For example, VectorMagic does a great job

I agree with Majenko that this would best be answered on gd.stackexchange.com. However, here are some tips:

• Vectorize the image as Gregory mentioned. VectorMagic can do this, but so can Illustrator and some free online tools like Aviary Raven.
• Convert to grayscale, then posterize, and then use a gradient map to recolor the image. This usually works better than plain posterization (especially on images with lots of noise), but for some images you may need to manually change color regions with with the same luminosity.
• Create separate layers for the different colors. You can then adjust the levels, shadow/highlights, or use multiple posterize passes to get better color boundaries. This can also be combined with the above processes. Recording a macro for this process can speed things up.
• Use higher quality images. There's no one-click solution to turning a low quality (i.e. lo-res, scanner/photo noise, bad/uneven lighting, compression artifacts, etc.) into crisp, high quality images. That's why most professional illustrators manually digitize their illustrations (make hi-res scans of their sketches and use a digitizer tablet to digitally trace the lines and color it) or just draw digitally from the get go. It's just easier to draw the illustration digitally than using a bunch of filters to try to convert analog artwork into something that looks like it was drawn digitally. It will never look as clean, and it's a lot more work than simply creating the illustration in a vector image editor like Illustrator in the first place.