La Sylphide and Giselle are ballets with very similar and also very different attributes. Dance-wise, both were revolutionary in that they introduced the idea of weightlessness and floating on the tips of the toes. This goes along with the Romantic Era. Plot-wise, they both involve forbidden love and the supernatural mixed together with tragedy at the end.
The biggest difference for me was the feel of the magical part of the ballets. In the second act of Giselle when Giselle turns into one of the Wilis, the whole ballet turns dark and tragic. The sylphs are always much more light hearted than the Wilis because they are not searching for revenge, and the second act keeps that feel going. For instance, whereas the Willis are in a graveyard and have somber expressions, the Sylphs are simply in the forest and have lighter, more easy-going expressions (until the main sylph dies). There is definitely more of a scary feel in Giselle and a simple sad feeling in La Sylphide.
This video portrays the light-hearted feel of La Sylphide (excluding the witch and the death at the end).