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I strongly suspect that they're still a lot better off than native speakers of (say) Mandarin or Korean or Japanese. To be more specific: I suspect German is somewhat better for this purpose than Italian, which in turn is substantially better than Russian, which in turn is substantially better than Hungarian, which in turn is substantially better than Mandarin.
I would guess (but don't know enough for my guess to be worth much) that the gap between Hungarian and Mandarin is substantially the largest of the ones above, and that one could find other languages that would slot into that gap while maintaining the "substantially better" progression.
Agreed.
I don't think the writing system would account for that much of a difference, since learning the Latin Alphabet is something everybody is doing anyway, and it's not much extra work (compared to grammar and vocabulary). I still suspect Hungarian-speakers might find English easier because of closer cultural assumptions and background.