Hello Elysa, I would say that: しんせつ: It mainly refers to the kind action one took and maybe it is often used to the people unfamiliar or unknown: e.g. when someone picked up your purse and brought it to you all the way to your house (this is just an example, this doesn't happen in Tokyo at least, you hand it to the police nearby) やさしい: It refers to the nature of one person, usually someone you know well. e.g. あなたはやさしいですね。(You are a kind person.) You never use しんせつ for referring to one's personality. You use when your friend doesn't sqeak ill of others, when your friend is brave to speak for you, etc. Hope this helps and please excuse my English.

e.g. 「しんせつな(親切な)」 親切なもてなし hospitality 親切な行いは褒美として大きなハグをもらえます。 A good deed gets rewarded and earns a giant hug. その村を訪れたとき、温かくて親切な人々と知り合った。 As I visited the village, I got acquainted with the warm and hospitable people. 私は彼の親切な行為に対して思いがけない褒美をやった。 I gave an unexpected reward for an act of his kindness. 「やさしい(優しい)」 彼はいつも優しい口調で話します。 He always speaks in a sweet tone. 彼女は優しい性格だ She has a gentle nature. 優しい言葉をかけてくる人に用心しなさい。 Be careful of sweet-talkers. 彼らには愛情と優しさが必要である They need love and tenderness. 湖の周囲の道を歩いていると聞こえるのは優しい風の音だけだった。 Only the voice of the gentle wind was heard as I walked the path around the lake.