Install WordPress MU at a new domain name?

I have a website directory which has high rankings in Google and would like to allow members that are listed on the website to set up a blog using WordPress MU.

I believe that it is best to use subdomains for each of the directory members. My main question is whether I should install WordPress MU in a subdirectory of the website or if I should install WordPress MU at a new domain name?

My question is mainly with a view towards SEO and increasing incoming links to original-branded-directory.com. I am wondering if it would be more beneficial to set up WordPress MU at a different domain name.

Which one should I use?
1) blog1.original-branded-directory.com/WordPressMU
2) blog1.different-domain-name.com (where WordPressMU could be installed in the root directory)

Also, my existing website directory is in a shared hosting account which allows add-on domains. If the answer is to install WordPress MU under a new domain name, would it be beneficial to use a separate hosting account?

Thanks.

Both ideas can work for SEO
You can always add links to the bottom of every page with .htaccess file and point them back to your other site.

Use another hosting account in case the Wordpress MU site uses to much bandwith or cpu and get your hosting shut down so your main site stays up.

Thanks! Can you tell me what to put in the .htaccess file to do that?

They should actually have the same effect. Though I've heard of some speculations that this will change in the future, SEs see subdomains as different sites from the primary domain i.e. blog1.original-branded-directory.com and original-branded-directory.com are different sites. There's no SEO benefit to purchasing a new domain over using sub-domains with your primary domain.