禧 is more formal/literary than 喜 (xǐ, joy/wedding). It appears mostly in set phrases like 新禧 (New Year's blessing) and 福禄寿禧 (fortune, prosperity, longevity, joy).
history
慈禧太后 (Empress Dowager Cixi, 1835-1908), the de facto ruler of late Qing China, used this character in her name — meaning 'compassion and joy'.
