As happy owner of both FAA and EASA IRs, can I inject a note of common sense.
1 - what you can log is different in the two regimes. You have to pass air law in each, so there's no excuse for not knowing both rules.
2 - if your logbook doesn't allow for different logging, modify it. If it hasn't got enough columns, buy another logbook.
3 - electronic logbooks help a lot. But, make sure that you use one that'll accommodate multiple authority logging requirements.
4 - for EASA you need two columns: flight by sole reference to instruments, and flight under IFR. THEY ARE NOT THE SAME.
5 - for FAA also log number of approaches, what approach, and where. EASA do not require this, but there is clearly no disbenefit in having that information.
G