Well, having been a Social Science major and a Journalism minor who has written several academic papers and worked for a variety of newspapers and magazines here is the difference for me.
In academic writing you generally introduce a topic by presenting a thesis or a hypothesis, then you lay out the premise of the discussion, then you discuss the topic and then review the discussion. In other words: You tell 'em what you're gonna tell 'em, you tell them, and then you tell 'em what you told them. The 'meat' of the discussion will generally be in the middle or towards the end.
In journalistic writing you write in what's called the inverted pyramid style. The 'meat' of the article will almost always be in the first paragraph, called the lede [or lead. Sometimes called a whatta (as in "what it's all about") or a nut graph, as in ("in a nutshell")]. The lede should be a paragraph that's so dense it could choke a horse. If you read nothing but the lede you will still know the who, what, when and where of the story.
After the lede you follow up with the how and -maybe- the why and other information of secondary and tertiary importance. If you've ever heard the phrase "buried the lede", that's what happens when you lead with interesting but less important information and the stuff of primary importance is 'buried' deep inside the article. This tactic is useful for academic writing but it's antithetical to journalistic writing. One other big difference is that instead of putting a nice summary conclusion at the end that neatly wraps everything up, like an academic paper, your journalistic article will simply stop at the end when you've run out of useful information.
The reason for this top-heavy style difference is twofold: One, readers of newspapers and magazines (this also applies to web) will generally stop reading after a few paragraphs. If you "bury the lede", the reader will stop reading before they get the most important information. Two, Copy editors realize they have limited space, especially in print. So when it comes time to chop your article to fit they aren't going to read the whole damn thing and edit it to make sense - they're just going to lop off as much stuff as they need to off the end assuming you've placed the most important stuff at the top. If the important bit is at the end, there's a good chance it'll just get cut or never even be read.
There are other differences, of course. Journalistic writing should be simpler and more accessible to the general public than academic writing. It doesn't have to be Dr. Seuss but it should be easily read by an educated 10th or 11th grade high school student. You should also keep in mind that your job is merely the inform the audience and present a balanced viewpoint; it is not your job to advocate for one side or the other. That's what the opinion page is for.