yes. I don't know the difference in meaning, and I'm Polish living in Poland.
the grammatical difference is that "tak" describes verb (or adverb) while "taki" describes an adjective.
Actually "tak" works both for adverbs and adjectives while "taki" for adjectives only.
Example from Polish wiktionary: "(1.2) Te góry są tak piękne/takie piękne!"
"masz takie oczy zielone" check this sweet song by Demarczyk: https://www.youtube.com/watch?v=yxmnTqYXLKU , I just love that song. But about your question, it seems to me that "taki/taka" makes the sentence more personal. "jesteś tak piękna" sounds more lofty than "jesteś taka piękna"