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Data transfers from old iPhones to new, may be done through iTunes, or through iCloud.
(Which method have you tried, and found to fail? if it failed, also, what was the full and exact error message that showed up, please? these are important details.)
The message about software being too old, may have appeared if you have an old version of, I don't know, editor or text messager or email on your old iPhone, and the data files that go with that old software aren't compatible with the newer types of that software on the new iPhone. It depends upon the exact error message, and the full context e.g. of what data you are trying to move, when the error showed up, how much data got moved, and so forth.
(Note: check whether *some* data, at least, got moved to the new iPhone. If so, which data.)