I don't wish to engage in standard HN negativity, but I'd like to suggest that you should probably don't want to use a carousel at all most of the time. From the user's perspective, a carousel is just a random image. You'll get more conversions if you choose the best image instead of a random one. http://www.bayesianwitch.com/blog/2014/carouselsarebadforcon...
If I'd get to redo the public website of our research institute, I'd add a carousel, because it looks cool and modern, and it allows you to showcase the work of different people without favoring one person by giving them the "best space".
And even if you have something to sell, it might be valuable to "wow" your potential customer, and to give them the impression that you are "cool" and "modern" and "state of the art" and have moving pictures of happy pretty professionals on your site.
Or, it might be better to have a big "BUY" or "DOWNLOAD" button in that space.
You can't generally say what's better for all use cases IMHO. You got to understand your visitors/customers, do testing if you can afford it, and so on.
Also, the main reason why carousels suck in my opinion, the bad usability (no touch, unclear if clicking moves to the next picture or opens another page, not clear how to move to other pictures) seems to be fixed nicely buy this script.