hello.
A fundamental difference between "~だろう!?" and " ~だと思う?" is a context that these phrases are used.
1. ~だろう!? ,for example
・お前は寿司(sushi)が好きなんだろう? (confirm a fact . In this case,a person who asks this question
is not sure whether he/she likes sushi.)
* By adding a exclamation mark,it will be a interrogation. it is often employed when a person is angry.
2,~だと思う?
・it is translated as a very simple sentence "Do you think that ~?".