With the ECB and the Bank of Japan (BoJ) both implementing large scale QE programmes, and the Fed still likely to announce its first rate hike later this year, both the euro and the yen are likely to depreciate against the dollar in the coming months. But the yen is likely to fall a lot further than the euro this year.
Reason being Japan monetary policy is likely to be loosened more, and earlier, than widely anticipated whereas it is highly unlikely that the ECB will spring any surprises. Also markets are likely to focus on the early benefits of QE in the euro-zone but its apparent failure after two years in Japan.
According to Capital Economics - "The yen will fall much further than the euro. Our forecasts are for the Japanese currency to weaken by 17%, to ¥140 per dollar, by year-end and for the euro to depreciate by around 8%, to parity against the dollar."
