The 2.0TDi's are all common rail where as the 1.9 before it wasn't. Some of the 1.9s were a conventional diesel distributor pump and could be described as adequate, but later PD 1.9s were a different beast and generally a good engine. There was 130bhp versions of this engine and I'm pretty sure there was also a 150bhp version in a VW car too.
Not entirely right.
The earlier 2.0 TDIs are Pump Duse engines (NOT common rail) and they are effective but ear bendingly loud/aggricultural, especially in the A3 which has S*** sound insulation. I know as we have one on a 56 plate and it's shocking – I'd choose my diesel Ford over it for just about any journey.
The more recent 2.0TDIs are common rail (about 2 years or so IIRC) an Audi dealer would tell you.
The 1.9TDI engine was originally a normal TD, it then gained the PD technology, which was designed to achieve the same effect as a common rail (ie really high injection pressures) but in a very different way.
There were 100(?),105,110,130 and 150 HP versions at various points in its life – you can tell which is in the car by the number of red letters in TDI on a VW (eg my wife's old Bora was a 130 so had a red D and I).
The 105 HP version remains as a very frugal, refined engine (partly due to its lower output I suspect) in the current model range – essentially it's the budget diesel option. This a great set up and I had it in a Mk5 Golf, in which I did 30k+ a year but it won't set your world on fire.
I'd rate the Golf over the A3 for value and to drive and its more useful (better room in the back, taller doors, boots are similar).
On topic… Golf GTI (Mk5) or Focus ST would be my choice.