The 1.8TS capacity is only 1747cc compared to the 2.0TS/JTS capacity of 1970cc, that is over 11% less.
The rated power of the 1.8TS engine is 144PS compared to the 2.0TS's 155PS, that is over 7% less.
The rated torque of the 1.8TS engine is 144Nm compared to the 2.0TS's 169Nm, that is nearly 15% less.
I would choose a 2.0TS any time over the 1.8TS.
Why the fuss about balancer shafts and belt I don't know; according to my old 156 handbook the 2.0TS weighs an extra 20Kg, probably that is due to the balance shafts, can't really see it could be anything else. The 156 weighs an extra 1.6% with the 2.0TS engine, insignificant when the extra power & torque is taken into account.
The JTS engine did have a lot of coking-up problems in its first incarnation but the later euro4 engine had new camshafts, piston rings, ECU, etc. and is far better (the GTV never had the euro3 engine). I should imagine the earlier GTs did have the euro3 engine, but 2004 or later cars should be OK.
There are more problems with the JTS, it is a more advanced & complicated engine than the TS having 4 instead of 2 lambda sensors, direct injection, lean-burn at low revs, higher compression ratio, etc. One of the problems is that the injectors operate in an extreme environment and so really need changing or at least cleaning after about 60,000 miles. I changed mine at 72,000 miles paying £100 each for a set + 4 hours labour to fit, but there was a very noticeable increase in overall performance.
Comparing the 2.0TS to the 2.0JTS, the most noticeable difference is at low revs, the JTS pulls like a tractor, it has massive diesel-like torque when pulling away but no diesel-like almost instantly running out of revs. At higher revs it is practically identical to the TS in performance, but you cannot feel the various stages (inlet manifold length change, valve timing change) coming into action so is less exhilarating.