it's not exactly the same; while 보고 싶어 means plain and simple "I miss you"/"I want to see", 보고 싶은데 can mean something like "but i miss you" or "(although I didn't think I'd feel this way) I miss you" depending on the context

오. 이해해요! 감사합니다!!! Unfortunately I don't remember the sentences that followed it!

Do you remember the following sentences? and the nuance? It depends on those. 1. The word "보고싶은데" can be used with sentences of the negative meaning in the context like: I want to see you but I am so busy. So, I can't. ( 보고싶은데 + the reason why I can't see you. ) 2. A: I have something to do tonight. B: I want to see you tonight...... But if you are busy then that's fine. ( The word "보고싶은데" can connote the understanding of the circumstance can't be helped. ) It depends on the nuance. It can connote the feeling 'upset'.