1. The site loads much more slowly
2. Facebook did not think enough about how their box should look like,perhaps with a little more interesting design.BUT no this is the usual blue box with a thin outline, sorry but in many cases it is really ugly in many sites.
3. Traffic that contributes Facebook like box is clean and simple drop in the ocean, instead you become traffic carrier for Facebook. Congratulations.
4. In 90% of those Facebook Like box are visible people or avatars of people who are honest words sometimes damage the image of your site, instead it upward.
5. (Not proven) Google NOT likes sites with Facebook like box For the above reasons.
So your choice is whether to bet on the box, or simply to get rid of it.
P.S. (4) This does not apply to all sites. There are sites that bring a serious amount of traffic.