Clearly we are not pronouncing them the way they were meant to be. The Gemara says that someone whose Ayin sounds like his Aleph cannot Daven by the Amud. Who are we left with?
The Teimanim are probably the closest to the original but it’s hard to tell. Although we can pronounce many consonants and vowels that our neighbors cannot, it was not always this way, especially after many generations. And without realizing it, American English affects our pronunciations, too.
Speaking a language shapes your mouth. Every language utilize the mouth muscles in a different way. The Hungarian and Upper German squaring of the jaw while pronouncing OO ends up sounding like EE to us. Once a generation is brought up not being able to pronounce proper Ü it merged with the EE.