Two main advantages come to mind:
1) being a low impedance system it's much less susceptible to induced noise than an inherantly (comparatively) high impedance voltage source.
2) with 4 - 20 mA you get easy checking for wire breaks - you get this with 1 -5 V as well, of course, but it's not so easy withh 0 -5 V or 0 - 10V setups.
another advantage is that given isolated inputs you can pass the current through several devices, for example panel meter, trend recorder, etc. as well as the PLC input. How many depends on the available voltage, but up to three devices is usually no problem.
Personally, given the choice, I would always go for 4 - 20 mA, unfortunately, I don't always have the choice! bawling
PS just noticed you're in Newcastle, my Dad lives in Consett, I was over visiting last March - not far away.