I think the other answers thus far are good, but can certainly be added to. I find projects and choice tend to work well within guidelines so they meet certain standards, but take more ownership of their work. Any time their project is seen as "authentic", they tend to work harder. For example, my students worked much harder on books we had published than on stories they just turn in to me because a book is a more authentic product.
Differentiation tends to be done based on either ability level or interest level or a combination of the two. One project I love and my students love even more is the tic-tac-toe (which can be skill and/or interest differentiation). You choose 9 projects on a common theme, skill, or idea. These can be small (do the whole thing in a day) or large (each project might take a few days). I like to organize mine based on different intelligences strategically arranged to let students have some work in their comfort zone and then to have to push themselves for others. Students choose three projects based on the rules of tic-tac-toe--three in a row. An easy way to differentiate based on skill level is to have a box that's the easiest level, one in the middle, and one that's more advanced. You can make your advanced kids choose one of those harder boxes; your struggling learners might have to choose one of the easier boxes, but they can choose their other options. This gives them choice while still letting them work to their ability.
One thing I've found most helpful in differentiating instruction for students is both me and them understanding their multiple intelligences (we call them our smarts--I work with middle school kids). We take tests to determine their strengths and weaknesses, and then we talk about strategies that can help them study and succeed based on their smarts. Most kids are not word smart/linguistically intelligent as their strongest skill set, but that's what most study strategies teach, so it sets up lots of kids to fail. By helping identify their strengths with specific strategies, it really helps kids succeed and makes it easier for them to take accountability for their own education.
If you're interested in any of the study strategies or tests to talk about with kids, let me know, and I can email you copies of what I use with my kids. It's probably best understood by kids in grades 3+.