I am NOT Korean but I do have over 500 grammar lessons from beginner to advanced. Here is the lesson on your question. Maybe it will help you. ~ (ㄴ)은데 ~는데 “But, however, so, and” Definition Introductory & Sentence ending > As an introductory ending means “but," “however,” “so,” “and.” indicating a consequent and relevant statement is next. > As a sentence ending it mean a different idea or another possibility, or it can be a signal for feedback. It must be interpreted from context what the speaker is inferring. > It can link sentences together in order to tell a story. Formation Vs + ㄴ데 to a descriptive verb ending in a vowel (present tense) (and the copola) *활발 하다 to be lively, to be active, to be full of life 화발 한데 He) is full of life… Vs + 은데 to a descriptive verb stem ending in a consonant (present tense). *귀찮다 to be annoying 귀찮은데 It is annoying Vs+ 는데 to a verb stem (action verbs, and forms other than the present tense) 쉬다 to rest 쉬는데 She is resting Sentence Examples 이 방이 더운데 (성풍기를 켜줘.) This room is a little hot… (please turn on the fan.) 이거는 맛있는데… (너무 싱거워.) This is delicious… (but it’s too bland) 이거는 맛있는데… (너는 어떻게 생각 해?) This is delicious… what do you think? 이거 무거운데, 들어줘. This is heavy, so please hold it for me. 저는 한국어를 공부하는데, 너무 재미있어요. I’m studying Korean, and it’s so fun. 나 부탁 하나 있는데 I have a favor… (infering: please listen) Notes  이다 becomes '인데'  Verb inflections are inflected before the addition of -ㄴ/은/는데. (e.g. past tense inflection: 봤는데)  If this structure is used as sentence ending, the politeness marker –요, can be added to the end (-ㄴ/은/는데요).

I think "보고싶어" means simply "I miss you." and, "보고싶은데" means "i miss you + and (or but) (+ etc...)" . "보고싶어" 는 (주어가 생략된)완벽한 문장이지만 (complete sentence) "보고싶은데..." 는 뒷부분이 생략되어 있어서 문장이 아니에요. (incomplete sentence)