The Cupra has the 'bigger' engine, with larger turbo, larger HPFP and some other smaller differences, but the biggest difference is the gearbox. Depending on the year the Cupra either has the MQ350 (manual) or a DQ250(DSG-6) or DQ381(DSG-7) which are all considered strong boxes that can withstand the power of the engine (especially when tuned, 400bhp our of a Cupra engine is pretty common, with supporting mods).
The 1.8 unfortunately has either the MQ250(manual) or the DQ200 (DSG-7) gearbox, especially the DQ200 is a VERY WEAK box, that even has difficulty handling standard power, let alone when tuned.
the Cupras are of course a little more expensive to buy, but also running costs are a little higher and insurance too. But if you can spend the extra money, I would always go for the Cupra.
I, on the other hand, did purposely buy a 1.8 ST, but recently have swappet out the DQ200 for a DQ250, which I already had planned for ever since I bought the car (the purchase price was too good to pass out on...). The swap was forced a little sooner then desired as I had planned this during my summer vacation, but unfortunately the gearbox shat itself already in May, forcing me to speed up the process.
But now I have the benefit of the strong gearbox, with the 'lighter' car, but the 1.8 engine can be tuned to almost same levels as the Cupra as the block itself is just as strong. So next plan is to swap to an IS38 (Cupra turbo) and Cupra/mk7R HPFP, together with a 3.5" DP and upgrade intercooler and have it mapped to about 380bhp.