The Williams was a special edition of the 16v and to be honest, I reckon the biggest difference in terms of costs is the insurance. The 16v is a Group 12; the Williams a Group 17.
The Williams had a few select mods to improve on the successful formula of the 16v. Engine wise, it was bored out to a 2.0 (instead of a 1.8, but they look the same when you open the bonnet) and had different bits internally - mainly from the 1.9 diesel of the day! This meant that there was more torque at lower revs - the Clio 16vs main failing. The Willy isnt much quicker than the Valver to 60 - you could close the difference with standing start technique. But the Williams is a bit quicker to the ton (at least 2 seconds quicker) - and it responds better at lower revs. Youve got to be over 400 revs to race anything and win in the 16v, but its different in the Williams. Theres not much more torque, but its always there - unlike the 16v.
Body, interior and components-wise, the two are very similar. The Williams has the same wide-arched shell and bonnet bulge and bits like brake callipers. The suspension is slightly differnt though, as is the clutch, g/box and diffs (I think).
The costs of running either are near identical. Fuel costs are similar, though the 16v is a bit better. The major thing is to get a good one. Both are fairly expensive to fix and things go wrong if theyre not cared for. There are plently of people who will confirm that!!
Generally, the Williams will be better looked after - it is a bit of an icon and there are only 1200 of them. That means that prices rarely go below £4k and youll be lucky to get a good one below £6k.
What swung the 16v for me was the greater choice, the availability of leather and the cheaper insurance and buying cost.