Just note that F360 is not *technically* a web application, but it isn;t exactly a traditional unconnected one either.
Your "files" get cloud stored so you have those disadvantages (it does have a cache of sorts, so if the net is down you are not *usually* left hanging on the thing you are *currently* working on), but you also don't get the advantages of a true web app like OnShape such as working on any os, any computer, any time with nothing to install, no upgrading and so on.
If you ever get over your distrust of webapps, definately give OnShape a try, I much prefer it to F360.