FWIW my FAA IR training (Arizona) was much harder than my JAA IR training (UK).
Except for NDB procedures on which one can spend more or less the entire conversion time...
But I would never recommend doing the FAA IR first and then the JAA IR to save money, because it won't.
Take the ab initio case. You might need to fly 40-50hrs to pass the FAA IR. Then you have 15hrs (min) for the conversion). It is not going to cost less than doing the whole 55hrs (MEIR) in Europe.
There is a better case where one already has plenty of instrument time, e.g. from the IMC Rating. Most UK pilots who did the FAA IR did it that way. The FAA IR takes that as a credit in full, whereas the JAA IR disregards all previous instrument time and training - unless you have a full ICAO IR. In this case you may be looking at say 20hrs on the FAA IR (I took 25) plus 15hrs on the conversion (I took 20). But it will be a lot more hassle and now, with the EASA screw-N-reg proposal due to come in April 2014, there is little point.
Nevertheless the FTOs here are pretty scared of conversion options being too easy, which is why the current EASA conversion proposal has (IIRC) 100hrs instrument time in it. This was obviously put in to stop large numbers of ATPL cadets doing an FAA CPL/IR and then converting over here. Each such case would likely reduce an FTO's income by maybe 25%, which is a lot of money.