These pair of words is really confusing because we all think that 'unreadable' means that we can not read something. Well, it's ok if we do that sometimes. But if we want to show a good level of English we should know that there is a small difference between these words.
We use 'unreadable' to refer to texts which are dull, badly written or difficult to understand. We pronounce it this way — [ʌnˈriː.də.bəl].
'Illegible' refers to the manner of handwriting itself. We can not read an illegible text because we can not understand what the author has written. We can not decipher it. We pronounce it this way — [ɪˈledʒ.ə.bəl].
For example 👇
The great books we’re expected to read that turn out unreadable. livemint.com
Wisconsin motorists with illegible license plates could get $150 fine but likely would be warned first. postcrescent.com