As Bigtoe mentioned, you can set the preferred domain to "www" in the Webmaster Tools.
As for the original issue of Googlebot not regularly crawling - I would suggest plugging in the other domain(s) for the site into Webmaster Tools and see if Googlebot is crawling there.
As for your competitors faring better than you despite using the same strategy - it can come down to you splitting your PR by having various links to either domain and maybe they only having links pointing at one of the domains - so they would not be splitting their PR. Or, maybe they have just been lucky so far.
Having multiple domains - mirror sites in effect - pointing at the same site is addressed in Google's Webmaster Guidelines...
"Don't create multiple pages, subdomains, or domains with substantially duplicate content."... and is well known to cause all sorts of ranking problems.
Also keep in mind that the duplication of title and tags issue that we noticed in an earlier thread impacts greatly your PR and Rank - so there are mulitiple issues here that will take time to be reflected in the serps once cleaned up.
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