I'm pretty sure that the C3 standard means that it complies with the C2 standard. Could be wrong of course
I don't think things are quite that simple. The specs are different, rather than one being better than the other.
Cars with the latest emissions control devices cannot tolerate the sulphated ash, phosphorus and sulphur content of earlier specifications & the challenge to the oil designers is to find ways of lowering the levels of these additives without compromising the performance of the oil.
In the old days, oil companies could get adequate performance from a cheap base mineral oil by chucking in a heap of additives (think Castrol GTX), but catalytic converters, lambda sensors, DPF's & what-have you would be quickly poisoned by this type of oil. Synthetics can achieve similar or better performance with a much lower level of additives because the base oil is so much more consistent & durable.
Many of the recent developments have been to find ways of maintaining oil performance whilst reducing the level of traditional additives by using alternative wear-reducing compounds, but not all of these are suitable for older engines, which is why we have such a plethora of different specifications today.
In reply to all those folks who've run xyz oil for huge mileages without blowing up their engine, I don't think the issue is so much about mechanical wear as about protecting all the hi-tech devices a modern engine needs to achieve its economy & emissions performance. Using the wrong oil probably won't wreck the bearings, but you just might find you need to fork out for a new DPF/cat/lambda sensor or whatever when you next visit an MOT station.
Unless you want to spend a huge amount of time researching the subject in great depth AND are prepared to use your car as an experimental vehicle, I'd suggest simply sticking to the specification (though not necessarily the brand) given by the manufacturer.
