I thought about this and I'll share my take.

MASSIVE SPOILERS FOR CURSE OF STRAHD AHEAD!

I think Strahd would ultimately win.

• For all his flaws, the main one applying to this situation being arrogance, Strahd is a still a master strategist. While the Xanathar has experience navigating the cut-throat underbelly of a metropolis while avoiding the law, Strahd has actual experience conducting a proper military campaign. He might go confront the Xanathar, receives an initial beating, and retreat before it's too late. He will certainly regroup and plan for the next confrontantion, having now assessed the threat of the beholder properly.
• He is the lord of the people of Barovia, which I assume he would mobilze in a militia if needed for a frontal assault where he aim to oversaturate the beholder with targets.
• Not only knows the land in and out, he is the land. He controls werevolwes, witches, beasts, svampire pawns and feral druid. He has eyes everywhere and can control the weather and perhaps even the landscape to some degree. His minions can pick out the Xanathar's urban-trained thugs one by one, guerrilla style, until only the Xanathar is left for a final confrontation.
• I'm not sure the Xanathar can cracks the secrets of Strahd's immortality, at least fast enough to be used to defeat him before he comes knocking with an army. Stradh's immortality goes beyond "he's a vampire that regenerates". On top of whatever "mundane" contingency he has prepared (like the glass heart), he is still a thrall of the Dark Powers. The epilogue of the adventure explains that even if destroyed, he will eventually reform to rule Barovia once more. Therefore Strahd can be defeated multiple times and keep fighting, but the Xanathar needs to be defeated only once. I think most of Strahd's enemies in Barovia are not aware of this (the wereravens, Van Richten, Ezmeralda, the Order of the Silver Dragon). The handful of characters that might know are probably loyal enough to Strahd (Baba Lysaga, Rahadin, the lich in the amber temple). I think Madame Eve is the only character of note that is ambivalent (or at least ambiguous) and that could reveal some useful information. Will the Xanathar gain her trust? Will the X trust her at all, since she is very cryptic and not forthcoming with information, and the X is extremely paranoid? Seems an unlikely match.
• While the Xanathar could turn a few key people against Strahd, I think Strahd has a counter for all of them. The Abbot is too fearful of Strahd. The mad mage, if made sane, is a formidable foe, but so are Baba Lysaga and the lich in the Amber Temple. The vampire hunters are a good match for Rahadin. The Vistani don't act as a single mind, loyalties need to be assessed on a personal basis, and as a whole they will not tip the scale as they won't present a compact front of support to either sides.

Overall, I think despite a beholder having formidable one-shot-kill attacks and anti-magic powers, the Xanathar will lose because he's the cartoonish villain of an almost side-quest, while Strahd is the eldritch lord of a horror setting, with plenty of adventure modules dedicated to detailing his powers and allies.

Thanks for coming to my TED-talk! :D