Is it worthwhile using an adapter to allow a PATA drive to connect to a SATA connector? Would it be better to just bite the bullet and buy a new SATA drive?
There is no real harm in using a PATA drive in your system over SATA but you might want to consider that the drive may be getting old. If the drive has been is service for a long time then replacing it with a faster SATA drive is probably a good idea. If you look at some of the drive failure rates you will find (depending on the Manufacturer of course) that after about 6 years 50% of the drives from a given lot will have failed (Backblaze study data).
For the first 1.5 years, drives fail at 5.1% per year. For the next 1.5 years, drives fail LESS, at about 1.4% per year. After 3 years though, failures rates skyrocket to 11.8% per year.
The primary reason SATA is used over PATA is because of the increased data transfer speeds with that SATA. PATA is capable of data transfers speeds of 66/100/133 MBs/second, whereas SATA is capable of 150/300/600 MBs/second. The speed differences are due to the various flavors of PATA and SATA, with the fastest speeds being the latest version of each currently available. You'll notice that SATA's slowest speed is still faster than PATA's fastest speed. So if you would like to have your system respond quicker move up to a SATA drive. Of course there is no reason you can't keep the old PATA drive as a place to store your backups (cough, cough, hint, hint).
The difference in speed between PATA and SATA is something I didn't know before. I'm doing my backups on external hard drives but thanks for the hint...