On the VAG cars (ie my skoda octavia TDI) the flywheel is in 2 parts, with the dampers and springs between them taking up the Shock when drive is transmitted. The OE clutch plate is solid, ie has no springs in it.
When you do a solid flywheel conversion, the flywheel is a solid one (surprise eh?) and the clutch plate is one with springs (ie a conventional clutch plate)
The only supposed downside is a tiny bit more vibration on tickover, but its gotta be less vibration than a fucked DM flywheel gives out.
Im having mine changed on friday cos the dual mass is fucked.
The skoda taxi boys had so many problems with the dual mass that Skoda UK actually list a taxi spec flywheel /clutch kit off the shelf.
The upside is because of the popularity of these solid flywheel conversions, that most factors now stock complete kits for most cars - my octavia kit is £180 incl vat (trade). The OE flywheel from skoda was £300+the clutch kit - its a no-brainer really.