I don't know of any significant controversy on this front; it is commonly accepted that the Uthmanic text was compiled during Uthman's lifetime, and that this was due (at least in part) to conflicts arising from Qur'anic variants that had spread throughout the Islamic world by that time.
Just the fact that the text was not only standardized, but standardized during the first generation of Islam while people who had been the original recipients of the message were still alive, gives a level of authority to Uthman's text that can't really be found in Biblical manuscripts. Pretty much every historical manuscript found is based off the Uthmanic text.
The Sana'a manuscript, discovered in 1972, contains examples of the pre-Uthmanic text, and is possibly the only preserved pre-Uthmanic text available. As expected, this contains many textual variations to Uthman's standard text.
That said, the means of transmission at that time — and for generations after — was still predominantly verbal, and the alphabet used at the time was, shall we say, incomplete. Even with the exact same text, there were still many ways — often conflicting — to read any particular passage.
There are now multiple readings (qira'at) of the Uthmanic text accepted by scholars; with no real consensus on which of them is most correct — given hadith reports that the Qur'an was revealed in multiple dialects simultaneously, it's quite possible that they're all correct — they are typically considered co-valid. Variant readings do exist, but these are generally rejected.