I have loads of crosshead screwdrivers. Some have pointy ends and some are flat... Some fit motorbike screws well and some just slip. I do have one screwdriver that fits Jap bikes perfectly - actually this is a lie - My stepson has one screwdriver that fits Jap bikes perfectly and it's a very short walk to his toolbox
Proper 'Phillips' screwdrivers are designed to slip when the screw reaches a certain torque setting, which unfortunately makes them practically useless for undoing said screws as they will slip...
I generally know which of my screwdrivers will be a good fit on other types of screw but if it don't feel right then it's a good sign that it's the wrong one.
I've heard people mutter about JIS screwdrivers being expensive - much in the same way that one bloke laughed when he heard I'd paid £20 for a set of drill bits cos he got his larger set for a fiver... Guess who's drills cut through metal and whose don't... So it's a case of 'Buy the best you can afford' and sometimes it's worth paying a bit extra.