There is no difference between the two. In fact web essentials leads to the same url. ie:
http://vswebessentials.com/features/typescript > http://www.typescriptlang.org/#Download > "Download the plugin" > http://www.microsoft.com/en-us/download/details.aspx?id=34790
Whic is same as > http://go.microsoft.com/fwlink/?LinkID=266563 > http://www.microsoft.com/en-us/download/details.aspx?id=34790
I prefer to download from https://typescript.codeplex.com/releases/ Since you get the even more cutting edge versions as well (e.g. you can get 0.9.0). But no difference between old versions (e.g. 0.8.3 are same at codeplex as MS site)