Is it easier to replace the internal hard drive of a PS3, or to go with an external hard drive?
It is easier to go with an external hard drive. That just involves plugging it in to the USB ports on your console and formatting it with the existing console OS.
However, installing a new hard drive isn't particularly complex. For most (all?) models of PS3 it's just a couple of screws, but it will mean a more-lengthy setup to install the software onto the console which involves downloading the OS onto a USB stick and going through several reboot cycles.
The PS3 also seemed, to me, fairly slow to create a partition for itself compared to trying to do the same thing on a PC. But my PS3 is one of the older models so I'm not sure if it's just showing its age.
Also, in the end result, I believe an internal drive will perform better (being connected via SATA) compared to an external USB-connected drive.