Recent data from our honeynet sensor grid reveals that the average life expectancy to compromise for an unpatched Linux system has increased from 72 hours to 3 months. This means that a unpatched Linux system with commonly used configurations (such as server builds of RedHat 9.0 or Suse 6.2) have an online mean life expectancy of 3 months before being successfully compromised. - Bruce Schneier

While no system will ever be perfectly secure, I do believe a modern Linux distribution is inherently more secure than the corresponding Windows computer. Studies have found that an unprotected Windows computer will survive for four (4) minutes on the Internet before being infected with some sort of malware.