Note: I'm going to try to do this without using technical terminology. If I start being too technical, let me know and I'm more than willing to revise!
Okay, let's get a few things out of the way. As you know, there is a scale of informal ⇔ formal in Japanese grammar. It is very similar to the scale of impolite ⇔ polite, but politeness is generally dependent on context.
So what does this mean for だろう and でしょう? Basically, the former is informal, the latter formal. If that's the only difference, why is だろう often considered "more masculine"? I would say that it has to do with what kind of language you're using in what kind of context. My overbroad generalization of the situation is represented by this table (where L is the kind of language used and C is the context):
Informal-C Masculine Feminine
Formal-C Impolite Polite
[Note: if anybody knows a better way to format a table, please let me know.]
Culturally and historically speaking, "feminine" speech is generally more formal (though there are certainly other features), while "masculine" speech is more informal (consider 俺、僕、私 and where each falls on the scales of formality and gender). So because だろう is less formal, it may be considered more masculine; likewise, because でしょう is more formal, it may be considered more feminine -- but mostly, it's about context. Using でしょう with your teacher or boss is not feminine. Using it with your friends may be.
So that's the answer to the first part of your question! Now let's move on to the third part. I'll come back to the second in a moment. You ask about the differences between these two sentences:
They are actually quite different. To answer, however, we'll need to analyze a third:
But wait! Aren't ～だろう and ～だろうか the same thing? The answer: no. The first is for confirmation ("Something happened, right?") or conjecture ("Something probably happened."), while by attaching か it becomes either a question ("Did something happen?") or wondering ("I wonder if something happened.").
～と思う, on the other hand, is simply used to express what one thinks. It contains conviction: "I think something happened," while ～だろう（か） is much more uncertain.
[Edit: Derek Schaab pointed out in the comments that this is a less than satisfactory explanation. Allow me to try again. Here goes...]
～と思う, on the other hand, offers one's thoughts. When you say ～と思う, you believe what you are saying; the same is not necessarily true for だろう (though it may be much of the time). It's difficult to compare to these two because 思う is for thoughts and だろう is more for guesses. ～と思う is always subjective, but subjectivity isn't an issue with だろう: it can range from completely subjective to based in solid fact.
Now that we have this out of the way, what is the difference between だろ and だろう? First of all, だろ is even more informal than だろう. But more importantly, I do not believe it can be used with か, though I may be wrong.
As for the actual difference in sound, the difference is that だろ is two morae, and だろう is three. Basically that means that だろ is the same length as みず, but in だろう, the "o" sound is twice as long, making it as long as みずが. The traits of short and long vowels in Japanese could be a question in its own right, however.