US HPS lamps are not compatible at all with EU ballasts for any wattage, even if they are nominally the same arc voltage. USA generally uses constant wattage ballasts, which are relatively immune to lamp voltage changes. Because of this the manufacturing tolerances for lamp voltage of USA HPS lamps are quite huge compared to the EU types. If used on the EU choke ballasts, which are highly sensitive to lamp voltage variations, those lamps will be proportionally over or under run. They will run at different power with consequences for lumens, colour consistency and life. EU HPS lamps can however be used on USA ballasts, because their voltage will always be much closer to the nominal value.
Even though that there are some series choke ballasts specifically designed for medium wattage North American high pressure sodium lamps, what is the precise explanation of North American 400W S51 high pressure sodium lamps being 100% incompatible with European 400W high pressure sodium ballasts and North American 250W S50 high pressure sodium lamps being incompatible with European 250W high pressure sodium ballasts? From what I see, I can hardly see any problems with interchanging North American 400W S51 high pressure sodium lamps with European 400W high pressure sodium lamps and North American 250W S50 high pressure sodium lamps with European 250W high pressure sodium lamps due to those lamps in particular having a similar arc voltage drop and operating current across lamp wattages. I was wondering if the 50Hz frequency of the European power grids has to do with North American high pressure sodium lamps being incompatible with European magnetic ballasts. In that case, should there be a significant reduction in service life of North American high pressure sodium lamps on 50Hz magnetic ballasts or any harm to European ballasts?