American "all purpose" flour vs. European "strong" flour: which is better for cinnamon rolls?

Which country are you in if you don't mind divulging that information? Some parts of Europe categorise wheat flours by gluten while others like France classify flour by potash content so to roughly figure out which is right for your recipe you should go by the protein content of the flour. You can probably find a close match to AP but might have to fine tune the recipe a bit.

Another thing to bear in mind is that all European butters have a higher fat content than US butter (unless you always shopped artisanal butter). In short that means that the butter is adding less liquid to the dough than the original recipe called for.

And another thing, did you bring your own measuring cups with you? The most widely available measuring cups across Europe are based on 250 ml like the Canadians, Australians and New Zealanders. A current US cup is 240 ml though older recipes call for a 237 ml cup. You can see how quickly the ratios can get skewed in a large batch of anything, especially if you're weighing butter because you can't cut it into tablespoons.

Still more, are you weighing the eggs you use? A large US egg weighs 57 g in the shell. This is the equivalent of a UK medium egg (a rare instance were the UK is bigger). Central Europe is more in line with the US. I'm not sure about southern Europe as I've never baked a cake there. Sometimes even subtracting a white or a yolk or adding an extra egg yolk can make all the difference.

I don't like using strong flour in sweet yeasted breads, but that's a personal preference. Unless left to cold rise I think it makes buns go hard faster. Again, just opinion. Not opinion though is that if you do use strong flour in a recipe calling for AP you will need more liquid or less flour least whatever you're making be very hard and dry. You'll need to pay close attention to the texture of the dough as you make it.

Take lots of notes as you bake and tweak your recipes and you will end up with a version that works with local ingredients.

Yes. Strong flour is for breads. It's good for cinnamon rolls. I always make mine with bread flour. (They may cook quicker too.) BTW, sponge cakes are designed to be dry, it's not the cake flour.

strong flour, I believe is similar to our bread flour; higher gluten content.

I wouldn't think the strong flour already contained yeast though.

I would, yes.

Never seen cake flour in Europe!