I'm not a tyre expert unfortunately 
I thought directionals were good in the wet, unless you fit them on the wrong side 
OK, everyone knows the Goodyear GSD3 (don't they?

) - anyway, these were 'directional' - and could be identified with a Y shaped tread pattern. Both shoulders of the tyres were identical - but they had an arrow on the sidewall indicating which direction they should be rotated.
But asymmetrics are very different - when you look across the whole surface of the tread, from one shoulder to the other, one side will be very different to the other. On one sidewall, it will say 'outside' and on the other, it will say 'inside'. On the more expensive tyres, they generally use two different rubber compounds - a harder compound on the outer edge, to cope with the increased loads when cornering, and a softer compound on the inner edge, so the tyre can disperse water and provide a degree of 'flexing'.
Google images of the GSD3 and the Michelin Pilot Sport PS2.
