If you've been in debate more than a few days you've probably already heard this, but it's worthwhile to point out all of the reasons that these activities are really not all that different. They are both forms of competitive debate, and (depending on where you live) there are excellent opportunities to compete in both at the Local, State, and National Level. Neither activity is considered "better," "smarter," or "harder" than the other by anyone who matters. Competing in either activity gives you the opportunity to develop speaking, researching, strategic, and critical thinking skills that is pretty much unrivaled, in my humble opinion.
So. Differences. Well, in policy you have a partner and in LD you don't. For most novices I think that this is the biggest determining factor because it's the one you best understand. You know that working with a partner can be infuriating, but it's nice having someone who's "got your back." Similarly, Working on your own means you get all the glory, but you're on your own out there. Now, these are all true, but they tend to matter a whole lot less than you think. You have to work in groups in both activities to prepare arguments, and in either activity you are going to have to pull your weight if you want to win. Most debaters tend not to stay with the same partner for long anyway as novices, so don't sweat the partner dynamics too much.
Now about the topics. The way I've always heard this is you debate "Questions of policy" in policy debate and "questions of value" in LD. This explanation tends to favor policy in most kids' minds, because most kids at least some fleeting idea of what policy means, while "value" is kind of vague. The hard part is, once you start explaining LD with words like "ethics" or "philosophy," kids get the impression that LD involves questions like "What is beauty?" and they run for the hills.
Interestingly enough, the two types of debate have covered some of the same subject matter over the years of resolutions, so I think the best way to compare and contrast the different debate styles is to look at how they approach the same topic. For example, take this pair of resolutions:
Policy Resolution (2009): The United States federal government should substantially increase social services for persons living in poverty in the United States.
LD Resolution (2008): Limiting economic inequality ought to be a more important social goal than maximizing economic freedom.
Both of these resolutions deal with the question of income inequality, but the different phrasings lead to different sets of important arguments. The LD resolution asks the general question of whether limiting inequality "ought" to be more important than economic freedom, while the policy resolution asks debaters to evaluate the merits of a particular type of action (social services) to limit inequality. The policy resolution is rooted in a particular place and time, meaning that arguments must take the present-day US into account, while arguments in the LD resolution can be somewhat disconnected from any particular society's laws or culture.
Another important difference is that the Policy resolution specifies a particular actor, IE the United States Federal Government, and the LD resolution does not. Some LD resolutions will specify an actor (though sometimes a more abstract actor, like "a just society"), but all policy resolutions will. This further constrains the debate to the limitations of that actor. Most policy debate rounds are further constrained by the particular plan the affirmative proposes, while LD debaters tend to defend/attack the "whole res."
Notice also the weighing systems in both resolutions. The LD resolution asks us to pick a "societal goal", something an entire soceity should strive toward. The policy resolution just asks us the bare "should?" This is implicitly asking: "The affirmative's plan, is it a good idea?" Now, the aff's plan might be a good idea because it meets some societal goal, but the policy resolution doesn't ask us to debate the goals themselves, at least not exclusively.
There are some other differences (time limits, how often the topic changes), but these are bad things to base a decision on, in my opinion. If you love LD debate, it's because you love debating LD resolutions. Same goes for policy. You could make policy a 1-on-1 activity with rotating bi-monthly topics, and policy debaters would still want to debate policy. They love the subject matter, not the set-up. You don't have to pick a favorite exclusively, and you definitely don't have to know right away, but you should play the game that excites you, debate the things that you feel need to be debated.
This is fuzzy, but LD debates tend towards the general case, the underlying decision-making systems. Policy debaters seek local truths, predictions of the future based on the world we live in. Remember this scene in Office Space?
Peter Gibbons: Our high school guidance counselor used to ask us what you'd do if you had a million dollars and you didn't have to work. And invariably what you'd say was supposed to be your career. So, if you wanted to fix old cars then you're supposed to be an auto mechanic.
Samir: So what did you say?
Peter Gibbons: I never had an answer. I guess that's why I'm working at Initech.
Michael Bolton: No, you're working at Initech because that question is bulls*** to begin with. If everyone listened to her, there'd be no janitors, because no one would clean s*** up if they had a million dollars.
Samir: You know what I would do if I had a million dollars? I would invest half of it in low risk mutual funds... and then take the other half over to my friend Asadulah who works in securities...
Michael Bolton: Samir, you're missing the point. The point of the exercise is that you're supposed to figure out what you would want to do if...
[printer starts beeping]
Michael Bolton: "PC Load Letter"? What the f*** does that mean?
Micheal is a LD debater. Samir is definitely a policy debater.