Should I use CO for all output or is PS better for some?

If I process images for web I use Photoshop to make a small thumbnail with a crop which is always likely to be a different crop than the original. CO Pro doesn't do that for me but when I process my images I always output a TIFF, Large JPG, Med JPG and a Web JPG which will be resized to hieght 550px.

I would like to know if it would be better to use CO Pro to output a single TIFF file and then use Photoshop to get those other files? Or to ask another way, should I let Capture One make all the images straight off the RAW file - inlcluding the resized image, or will I get any improvement in giving Capture One the RAW conversion and PS the subsequent file conversions?

Thank you

Martin

PS - this isn't about the RAW conversion. I would only use Capture One for that.