1) いっしょに〜しませんか？(Shimasen ka?) = wouldn’t you do (something) with me
2) 〜しましょうか。(shimashou!) = Let’s do (something)
They are very similar but ~Shimasenka has a more polite nuance and difficult for people to answer “No”. はなみをしませんか？ Wouldn’t you do Hanami with me?