To put it very broadly, ばしょ is used for physical places whereas ところ is more versatile and can be used to indicate not only physical place but also time and abstract "place" like 君の優しいところが好き is saying "the place/aspect I like about you is your kindness"
Both! :) It really depends on the context and what you want to say. If you look them up on the Renshuu dictionary, you’ll see they have slightly different definitions, like howところ can be used to mean someone’s house whereas ばしょ not so much. ばしょalso often has the feeling you’re referring to a specific place or location. The example sentences in Renshuu dictionary are very useful for getting a feel for how they’re used differently… good luck!
