I was watching American national news coverage of the "Brexit" poll, and it seemed to me that none of the news anchors nor commentators used a voiced consonant cluster in their pronunciation of the word. That is they all pronounced it /bɹɛksɪt/ and not /bɹɛgzɪt/. Upon discussing the poll with two American friends, I realized that they too use the voiceless pronunciation. The older of the two even defended his rendering of the word, saying, "It's spelled with an ex."
Merriam-Webster, the Oxford English Dictionary, and Dictionary.com list the voiced version of "exit" first, so I would assume it's the more popular or traditional one. Although the spelling and latin origin would lead me to believe the voiceless pronunciation is conventional, "exotic" and "exhaust" both have those qualities too and only have the option of a voiced cluster.
What is the frequency of the voiceless consonant cluster, /ks/, versus the voiced one, /gz/, in "exit?"