Feature matching uses the feature descriptors to match features with one another (usually) using a nearest neighbor search in the feature descriptor space. The basic idea is you have descriptor vectors, and the same feature in two images should be near each other in the descriptor space, so you just match that way.
Optical flow algorithms do not look at a descriptor space, and instead, looks at pixel patches around features and tries to match those patches instead. If you're familiar with dense optical flow, sparse optical flow just does dense optical flow but on small patches of the image around feature points. Thus optical flow assumes brightness constancy, that is, that pixel brightness doesn't change between frames. Also, since you're looking around neighboring pixels, you need to make the assumption that neighboring points to your features move similarly to your feature. Finally, since it's using a dense flow algorithm on small patches, the points where they move cannot be very far in the image from the original feature location. If they are, then the pyramid-resolution approach is recommended, where you scale down the image before you do this so that what once was a 16 pixel translation is now a 2 pixel translation, and then you can scale up with the found transformation as your prior.
So feature matching algorithms are all-in-all far better when it comes to using templates where the scale is not exactly the same, or if there's a perspective difference in the image and template, or if the transformations are large. However, your matches are only as good as your feature detector is exact. On optical flow algorithms, as long as it's looking in the right spot, the transformations can be really, really precise. They're both computationally expensive a bit; optical flow algorithms being an iterative approach makes them expensive (and although you'd think the pyramid approach can eat up more costs by running on more images, it can actually make it faster in some cases to reach the desired accuracy), and nearest neighbor searches are also expensive. Optical flow algorithms OTOH can work really well when the transformations are small, but if anything in your scene messes with your lighting or you get some incorrect pixels (like say, even minor occlusion) can really throw it off.
Which one to use definitely depends on the project. For a project I worked on with satellite imagery, I used dense optical flow because the images of desert terrain I was working with did not have precise enough features (in location) and different feature descriptors happen to look relatively similar so searching that feature space wasn't giving tons of great matches. In this case, optical flow was the better method. However, if you were doing image alignment on satellite imagery of a city where buildings can occlude parts of the scene, there are a lot of features that will stay matched and give a better result.
The OpenCV Lucas-Kanade tutorial doesn't give a whole lot of insight but should get your code moving in the right direction with the above in mind.
