If you've been keeping up with the latest batch of Batman movies, you're probably familiar with Two-Face, the good-guy-turned-villain from The Dark Knight who decides the fate of his victims by flipping a coin. For those of you who haven't seen the movie, the story of Two-Face follows a pretty typical plot line: good guy does good things, evil villain ruins everything by blowing up his girlfriend, good guy turns evil because he decides there is no logic to the world anymore. The poetic beauty of Two-Face is that half his face was scarred in the same accident that kills his girlfriend, so he's a physical embodiment of both the good man he used to be and the evil villain he becomes.
Now let's be clear—we are not trying to imply that the speaker(s) in "Up-Hill" are evil or sadistic (or even fans of Batman). We do think, however, that the way Two-Face is simultaneously two opposing people is a pretty good way to think about the voices we hear in this poem. On the most basic level, we have Speaker #1, who is full of questions, and Speaker #2, who is full of answers. It's easy to tell who is talking, not only because of the whole question-answer thing, but also because Rossetti goes to the trouble of making their lines different lengths (Speaker #2's are generally shorter).
We've got a lot of theories to choose from if we're interested in figuring out who these voices represent. An obvious one is that they represent two separate people—one who's going on a journey and another who's giving advice, having taken the trip before. Another common answer is that it's one person in dialogue with their own subconscious; the speaker is clearly nervous about the upcoming journey (the questions) but is also prepared (the answers), and the poem is a recreation of that person talking his or herself down from some pre-departure nerves. The third answer is that this represents Speaker #1's dialogue with some supernatural power, but even people who agree on this interpretation can't decide whether or not they think it's one person (the speaker and the voice of God inside of them) or two people (the speaker being one and God being the other).
The great thing about this poem (and the Two-Face analogy) is that there isn't a definitively right or wrong answer as to whether this is two sides or aspects of one person, or two separate people who happen to be weirdly in sync with each other. Your answer will change depending on the situation (if we're talking about Batman) or the poetic interpretation you choose to work with (if we're talking about "Up-Hill"). Just to prove our point, we've got a fun little exercise for you to try. Look in your pocket or purse, and take out a coin. Flip it. Heads, you argue it's one speaker; tails, you argue it's two. Ready, go.