There are two things to think of: performance and convenience.
There is no performance advantage for an external hard drive over your internal one. The drive itself is very likely the same unit. So if you already have enough drive space for your tracks then you are fine. If you have internal expansion space for an additional hard drive then you will save money by getting an extra internal drive.
The convenience advantage to having an external hard drive is that you can transport it from one computer to another. For example you can record on your hard drive at one studio then carry to another studio for other tracks and then to yet another for mixing.
However be concerned about interface speeds. If you are using a USB interface to connect to your audio interface do not get a USB external hard drive! Or if you do record temporarily to the internal hard drive and then copy it to the external hard drive while you are not recording.
edit...added following:
When looking at differences in cost they are likely to be caused by:
1. Different quality of the underlying drive, although if you look at the retail prices of drives they are pretty close from different manufacturers
2. Different interfaces. SCSI, Firewire, USB, USB2 all have different prices. USB1 is too slow for live recording.
3. Premium name brand and markup. This is probbably the largest factor.
4. Warranty...usually goes along with 3