EA888 (MkVI) is cheaper and easier (read: quicker) to build. There's been some debate as to whether it's stronger or not. On paper, the block (a different grade of cast iron) is supposed to be a better design and is stronger (boost friendly) whilst being lighter. However, I've been told by of a friend on the 'inside' that the tolerances are much lower and it's not as 'over-engineered' as its predecessor, i.e. ancillaries and other components can not cope when the power is turned up. I believe VWR have blown up a couple in the name of research but lessons have been learnt and power outputs are creeping up.
Late US model MkV GTI's also came with this engine, I would imagine for emissions and production reasons.
EA113 (MkV) is an older design (original design nearly 20 years old), but is arguably more resilient and can handle more power (in all of it's various guises). Development cost and lead-time were what drove VW to use the older engine for the current R models.
One of the more interesting features off the EA888 is the turbo. AFAIK, the European MkVI GTI still uses a BW/KKK K03. The current Ocatavia VRs uses the same engine but with an IHI turbo - which apparently sits quite nicely between the K03 and K04 in terms of lag and punch.
