What are the downsides to using Time Machine?
Here are some of the limitations you have to accept or mitigate if you choose Time Machine:


Time machine requires an apple specific HFS+ filesystem to store backups.
The backup isn't bootable.
The backup doesn't record differences inside a file. Large (database) files with tiny changes make each incremental save longer and move more data. This also can eat up storage space faster if these type files are not excluded and potentially backed up another way if they can't be regenerated after a restore (like mail stored on IMAP servers)
It must be an external drive or an official apple network destination like TimeCapsule or Mac OS X Server to be a supported by Apple. 
It will delete backups according to the official scheule ( hourly backups combine and expire after a day. Dailies expire after 31 days. Weekly backups can be deleted if there isn't enough space to contain the estimated size of the next backup.  In odd cases or if there is a bug, you could end up with all the history gone an one copy of the last backup. 
The destination volume must be larger in size than the boot volume. 


Once you are aware of these limitations, it's fairly easy to work around all but the first limitation with some planning and/or extra software / hardware. The HFS+ format for storage is pretty inflexible with no realistic mitigation or workarounds.