White Mexicans are genetically closer.
Modern Turks from Turkey average only ~9-15% Central Asian/Turkic ancestry (the rest is mainly Anatolian, Caucasian, Middle Eastern and Balkan/European). Original Turks from Central Asia/Siberia carried far higher East Eurasian components. White Mexicans are predominantly Iberian European (West Eurasian), matching the bulk of modern Turkish ancestry more closely than the original Turkic profile does.