I was thinking that it might be less confusing to visitors if the URL were along the lines of ecommerce.mysite.com, information.mysite.com and directory.mysite com, rather than having three completely different URL's.
I presume that by "completely different URLs" you meant three separate domains (versus creating new subdomains of the current pandalised domain).
I haven't really seen any advantage or disadvantage to subdomains as opposed to folders in search; but there can be ramifications for your analytics unless you set it up to track across subdomains.
I think that the OP reason behind splitting the site here is different one. If the main site is pandalised, with a suspect being "site focus" and "site classification", then from what I gather OP is thinking is that splitting the site in three different sites, each on a different subdomain (or domain), will give each of these sites more narrow "focus" and easier "classification", hence perhaps coming out of Panda not just for the spun-off new sites, but also helping the main site recovering from Panda as its focus would be more targeted.
The question here is - if the split is done over three subdomains, would Google still see these three subdomains somehow as "one site" and therefore they would remain pandalised, or would subdomains be treated as a completely separate narrowly focused sites, giving it perhaps a chance to get out of Panda. If the whole purpose of split is solely to have separate more narrow focus on each of the sites, and there is even small chance that G. would treat three separate subdomains as "one site" with regards to classification and focus, then it would be safer to choose three different domains (even though as dickbaker says, for the visitor it would make more sense to have subdomains).
I am none the wiser here with regards to splitting into subdomains versus splitting onto three separate domains. There has been other threads some time ago on whether subdomain inherits any trust, etc from domain and not only the opinions differ, but even if there was a concensus, this may not be how G. now sees subdomains & domains in Panda view.
With regards to handling it (canonicals versus redirect), if you use canonicals, this implies you are leaving these pages on the original domain too. If I was doing this move purely in attempt to get out of Panda, then I would not leave pages on the original site (assumes the use of canonical), instead, I would remove these pages and redirect them to the spun-off site.
If you truly want to move number of pages from the current site to a new domain/subdomain, then 301 should be used on a page to page basis. You could use this excercise in the same time to get rid of low value pages, by either combining some pages together (if it makes sense) or by just dropping them and leave the main site return 404 (or even better, 410).
Also, before deciding on such a move, inbound links must be analysed. If the section you are moving does not have many inbound links and relies on PR flow from the home page and/or other strong pages that now remain on the main site, then the new site that is a spin-off section of the old site may have very low inbound link power.
And lastly, I am not sure how the current site interlinks between the subject sections and if there is a current heavy interlinking, whether this would have an impact on split or not as there would be lots of links going to spun-off site(s).