Is EXILE pronounced like " EGZAIL" or " EKSAIL"
Dictionaries show two types of pronounciation but which one is more correct and modern?

And the same about EXIT and ALEXANDER.

Thanks in advance.
After sitting here saying assorted 'ex' words in various manners, I have concluded that in Britain these are usually pronounced Eks. In practise the sound variation is so tiny I would advise you keep with whichever one you can pronounce most comfortably. I doubt anyone will notice.
Personally, I say GZ for all three.

As for the prefix "ex-":

"ex-" followed by a consonant (other than silent 'h'): eks [excellent, expect, exhale]
"ex-" followed by a vowel (or silent 'h' plus a vowel):
a) when the "ex-" is stressed: eks [exorcise, exigent, exhibition]
b) when the "ex-" is not stressed (the next syllable is stressed): egz [exorbitant, exhibit, examine]

Exceptions: exile, exit!!! (coincidence?) (But these can also be pronounced according to the 'rules' above.)

This is American English, by the way. British English may be different.

Emotion: geeked
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Hmmn, thinking again, there are 'egz' words in British English too. The b) examples above apply.
Students: Are you brave enough to let our tutors analyse your pronunciation?
Jimmy Hetfield from 'Metallica' sings EXIT in 'Enter Sandman' with EKS.

So you say there's no much difference?