Well... XP only supports one login to the GUI, so it's sort-of more secure by a tiny margin when left logged in, as long as you have physical security (i.e. it's locked in a closet), otherwise, people could walk right up and abuse the PC however they like.

XP is far more secure shut off. In this arena, and this alone is Vista 'better'. But only for a while, until all the similar exploits are discovered in Vista... though Vista may win for 'security through obscurity'. If it remains largely unadopted, malware writers won't focus on it. Even at 10,000,000 copies, it's 1% of the PC market.

Another simple possibility is get a dedicated print server + NAS appliance. Your PC will eat around 200 watts day and night, or up to around 5KWh per day, and according to your utility fees for electricity, that could be over $.50 a day, or $180 a year.

A little appliance to do the same thing will eat 40 watts, and since it usually runs an embedded Linux on an oddball (cheap) low power processor and doesn't accept 'normal' computer connections and services, it's virtually immune to alien attack. Some don't cost a lot more than the hard drive they contain. Some can be bought 'empty' with the hard drive ala carte.
http://www.google.com/products?q=%22Network+Attached+Storage%22+printer

A dedicated print-only server takes practically no power and is dirt cheap, too.
http://www.google.com/products?hl=en&q=Network+print+server

So don't run your big, general purpose desktop computer to do what a tiny appliance will do in a closet. If it has a hard drive attached, be sure to put it all on a UPS. A cheap, tiny UPS will do. You can plug your wireless router, cordless phones and answering machine into it as well if you like.

BTW, Linux on a little subcompact notebook is another excellent option for a server. Plug a big USB hard drive into it, plug it into the printer, stuff it somewhere and forget it unless you need to make a change. You can even upgrade the tiny notebook internal hard disk to a reasonable size and you automatically get battery backup on it from the notebook's battery.