I see both positive and negative connotations for both. What is the nuance between the two?
Perhaps others in the community can provide a better explanation, but for me 잘 살아봐요 can have both a positive and negative connotation as you said, whereas 잘 살아요 has a positive connotation only. Here are some examples for 잘 살아봐요:
Positive connotation, when for instance a newly wed couple makes a vow: 우리 한번 잘 살아봐요. Let's team up and lead a good life for the both of us.
Negative connotation, when for instance a very angry friend-zoned man/woman says to his/her ex and archnemesis: 둘이 한번 잘 살아봐요, 그럼. Oh yeah? Let's see how long you two last. The stronger way to say this would be 둘이 한번 잘 살아보든가. It's stronger because there's no use of honorifics.
잘 살아요 from my perspective is almost always positive.
다들 잘 살아요: May all you lead good lives.
다들 잘 살아야지요: We all must lead good lives.
If we consider both as a suggesting sentence(I don't know the English word, but in Korean it's 청유형), Both of them would not be comprehended as negative meaning, ordinarily.
-아(어) 보다 basically means 'attempt to -' or 'try to -'. So, 잘 살아봐요 means like 'let's try to live happily', the speaker is adding the implication of 'trying', like he is facing a married life of future and regarding it as a task of life. But just 잘 살아요 doesn't have this kind of implication.
On the other hand, we can consider 잘 살아봐요 and 잘 살아요 as a imperative mood(명령형 in Korean), we may able to understand that they can have both positive and negative connotations.
Ordinarily, they are positive languages.
- 잘 살아봐요!/잘 살아요!(I wish you live happily!)
But at special cases, they can be ironies.
- 그래, 어디 한번 잘 살아봐라!
- 너 혼자 잘 먹고 잘 살아라!
These are words of curse, not a blessing.
But note that you don't have to worry about misuse between 잘 살아봐요 and 잘 살아요, they are almost same. The implication I explained above is not that important, it is just a theoretical thing, only to figure out very subtle difference.