Hi John
I too use the Mitchell resizing. I haven't tried any other method, so would be interested to see the replies you receive.
One thing I have noticed is that my images suffer more when I use the Mitchell method during the Optimise stage of Registax.
My images are better when I resize (using Mitchell) on the Final tab, right at the end.
I generally use a 1.5x Mitchell resize for greater image scale. I then take that image into Photoshop and boost the image size by about another 10% when saving for web.
I find this introduces less artifacts for some reason