Disk may not be able to match tape in density, but surely it must surpass tape in performance, right? Think again. The fastest current-generation LTO drives are capable of around 120MBps total throughput, while the LTO-5 standard extends this to 140MBps (uncompressed). Your average high-capacity SATA disk is lucky to get 35MBps. You'd need to stripe together four or five disks to get the same throughput.
The only other storage technology that can match this kind of sequential data throughput on a single media is solid-state disk (SSD), and at current prices and capacities, replacing all of your tape capacity with SSD would be, well, dumb. Tape wins again.
But the fact that tape can be removed, shipped, and stored for long periods of time is truly what makes it so popular. It's difficult to trust that a device with as many moving parts as a hard drive can endure being shipped to an offsite storage vault -- or sit in a cabinet for 10 years until you need it to run again. Tape, if handled correctly, can last 15 or more years and provide a bulletproof archive capability.
Given all of the reasons why tape dominates backup technology, why would anyone want to rid of it? Because it's inconvenient. To use your backup as a hedge against fire or natural disaster, backups need to be made onto tape at least once a day and then either stored offsite or in a fireproof safe. That means that some poor sap has to remember to go over and pop the tapes out and carry, ship, or drive them somewhere. Every day. Always. In an age where VPNs and remote management tools make it almost unnecessary to get out of bed to run an enterprise network, tape backups are one of the few remaining holdovers that require someone to physically go do something. How distasteful!
Another reason most administrators tend to dislike tape is the amount of time that it can take to perform restorations of small amounts of data. While backups are generally very fast -- the disk being backed up is usually the bottleneck, not the tape drive -- restores of a few tiny files can take a few minutes. This is due to the linear nature of the media: The tape drive has to spin its wheels to find the tiny little bits that you asked for. Hard disks are random-access devices that seek data in milliseconds, not minutes.
So what are the real tape alternatives? Virtual Tape Libraries are great pieces of hardware, but they aren't meant to replace actual tape libraries. VTLs just supplement tape as an immediately available restoration source and backup cache for tapes that are used for archival purposes. Even if you take advantage of some of the great replication features found in some VTLs, you still can't call that an archive, even if it is offsite. Just the fact that the remote VTL is connected to a network means that anyone with the right access, such as a disaffected administrator, can remotely destroy all of the data with very little effort.