Симпатия is a false friend of English "sympathy": it means "liking, fondness".
Likewise, симпатичный means "lovely, likeable".
Russian for "sympathy" would be сочувствие, сострадание, взаимопонимание, the first word being the Slavic calque of the Greek ancestor to the English word.
I can hardly imagine any context where "sympathy" could be translated as симпатия (or "sympathetic" as симпатичный).
Also, how does 'симпатичный' compare to 'привлекательный' in meaning?
Привлекательный is a calque of some cognate of "attractive" and means the same.
The two words are quite close in meaning, but привлекательный has more sexual connotation.
Симпатичная бабуля would mean "lovely old lady"; привлекательная бабуля would mean "attractive old lady". It would be weird to call an old lady attractive.