My perspective has changed on this since the 1990's. My answer was always use the longer full name. I now reach the opposite conclusion using some process steps.
Just a process note here -- Start by registering the half dozen or so you are considering. I have had clients that come to me after months of work only to find out the one they liked was registered before they decided. Really folks, if you don't have the $100 to keep the short list available during your selection process, you are not being serious about making a business.
Step 1. My TOP suggestion is type them out in a 16pt sans-serif font, each on a separate piece of white paper. Show them to as many people as you can, ideally in every cultural group you might target, and prepare to be shocked by what people think the domain spells or stands for. I have worked with clients who were stunned to find out their domain name was suggesting some unnatural act with a gopher.
Next hand the individuals a blank piece of white paper and ask them to write down the domain name. This is where you will start seeing the spelling errors. It is VERY common for other people to register the misspellings to bleed off traffic. For about $8 per domain per year, register the ones you recognize and point them to your domain.
TIP: I always suggest you also register the separate domain of "wwwyourdomain.com" as well. Visitors forget to put a period between the common "www" machine name and the domain name, which means they are putting in the WRONG domain name to try and get to you. Help them!
Step 2. If your company name has non-generic words, like a last name or something you made up, then make sure the shorter domain names are written with appropriate caps. Smith and Tillinghast Company might be written as STCompany.com, but again refer back to step one and make sure that (stcompany.com) doesn't spell something unpleasant.
The corollary here is don't use generic words in your company name (i.e. Worldwide Software) and expect that anyone will ever remember your name, much less be able to find you. If you feel you must use generic words, I recommend the long form of the domain (i.e. WorldwideSoftware.com)
Step 3. Only use ONE domain name. Whichever one you choose, long or short, only use that one for everything. You can point other versions ( short --> long, long --> short, misspelling --> correct), but don't publish more than one domain as it can confuse your brand.
SO a fair question is why do I now recommend the shorter version? Email! Millions of email get delivered to the wrong company (maybe even to someone who intentionally registered a domain name to siphon off some of your company's email). Make sure that people can type in your email address as quickly and accurately as possible. As someone mentioned above, most people will follow links to your web site, but people do still type in email addresses manually in a staggering number of scenarios. Your domain is about communication, but remember that is a two-way communication. Help your customers reach you and only you, and it should serve you well.
My suggestions: Shorter, watch for other meanings, written with appropriate caps, only ONE domain for your brand, register the misspellings, and be nice to gophers!
(no gophers were harmed in the making of this free advice)