No, Linux is not inherently less robust then Windows when it comes to sudden power outages. What could happen - in the case of either OS - is that stuff is being written to the filesystem on the harddrive at the precise moment power is lost, and (historically) this could corrupt the filesystem.
The solution to this problem is to use a journaling filesystem which is immune to this problem based on the way it writes information. Most new filesystems - including Ext3 and ExT4 (the most common filesystems for Linux), as, I believe, NTFS is as well. So as long as you are using a journaling filesystem you won't experience this problem.
Later on down the boot process, if you have a database (I'm looking at MYSQL, Postgres does not suffer from this), you may have analogous issues with the MYSQL database - MYSQL is often not particularly robust (Google ACID compliance MYSQL for this topic). You can get around this problem by forcing a check of the indexes on reboot if your MySQL setup is not ACID compliant.
Another (somewhat Jaded and possibly unfair to Windows) view might be this - Linux boxes are more reliable then Windows boxes (as measured by Uptime and the need to do reboots) - thus it is possible that when Linux boxes fail on reboot it is a hardware problem due to old age rather then a software problem - whereas a failing Windows box may be detected sooner because of more frequent reboots)