2003 Jetta Wagon with a manual is widely considered the best, but later ones have some advantages that the older ones don't, especially if you modify. Engine code is ALH, same as what you have now.
While the 2004-2006 Golf/New Beetle/2004-2005.0 Jetta TDIs do get slightly worse mileage stock, and are not tolerant of incorrect oils, they have higher injection pressure, IIRC are more tolerant of crap US fuel, and when modified can perform fantastically. Engine code is BEW.
The 2004-2005 Passats have the same issues with incorrect oils, plus a failure-prone balance shaft module that's expensive to replace (but there is a fixed design, at least), and expensive to rebuild front suspension. Oh, and a failure-prone mandatory automatic. Worse mileage than a Golf/Jetta, because it's a bigger car with a bigger engine. Very nice cars once you dump $10k into them. (OK, that estimate might be a bit high. But, it's not THAT high.) Engine code is BHW.
The 2005.5-2006 Jetta TDIs are bigger cars, with better suspension. Worse mileage, more size, better handling. You win some, you lose some. Engine code is BRM.
The 2009-2010 Jetta, 2009-2013 Sportwagen, 2009-2012 Audi A3, and 2010-2013 Golf are all the same basic chassis as the 2005.5-2006 Jettas, although with updated electronics in 2010+ cars, a stiffer chassis in Golfs, and updated styling in 2010+ Sportwagens/Golfs. The engine is an inherently more efficient design, but choked by craploads of emissions controls that hurt fuel economy and power, and reduce reliability (look at intercooler icing). Also, the high pressure fuel pumps seem to not be very tolerant of US fuel.
The 2011-2013 Jetta is a chassis loosely based on the previous chassis, but with suspension components from the 1999.5-2005.0 Jetta (and the Golf/New Beetle relatives) up front, and a solid rear beam. So, the suspension's worse. Interior trim is significantly cheapened. Engine is the same as the other 2009+ cars I've already mentioned, so all the same benefits and problems are there.
The 2013 New Beetle is basically a Golf with a weird body, and with Jetta rear suspension. So, that pretty much says it all.
Engine codes on all of the above 2009-2013 cars are either CBEA (for 2009s and for Audis) or CJAA (for 2010+ VWs).
The 2012-2013 Passat is based on the outgoing 2006-2011 Passat (and the current CC), which is in turn based on the previous Jetta and the Rabbit. Similar powertrain to the current Jetta, Sportwagen, Golf, A3, and New Beetle, but with modified fuel injection, and a different emissions system. The jury's still out on whether the fuel injection is actually tolerant of US fuel, but the new emissions system seems to work far better, reducing fuel consumption - Passats are able to compete with Golf/Jetta/A3/NBs on fuel economy. Engine code is CKRA.
So, the best of the newer ones... depends on what you want, really. But, I'd say that if you want a Mk4 still, it could go either way, ALH or BEW. If you want a Mk5/Mk6, I'll go with the BRM but say that the CBEA/CJAA may be better if you don't mind violating federal law, as well as only fueling from high quality stations and using lubricity additive. If you want a Passat, either go older (1997) or 2012-2013.
Oh, and any of those cars will have more rear seat and cargo room than your Beetle, except for maybe Mk4 Jetta sedans. Front seat, all of those will have less room, the 1998-2010 New Beetle has a ridiculous amount of front seat room.