Functional Differences :
1.BusinessObjects client needs to be installed on every PC from where you want to build / access reports. WebI needs just a browser & URL(of the server from where it will access BO).
2.BOMAIN.Key file needs to be copied on every individual PC that uses BO client. WebI doesn't need it.
3.You need to stick to those PCs which have BO client installed, WebI can let you access even when you are roaming anywhere in the world(provided the access conditions i.e. internet/VPN enabled WebI web server)
Architectural Differences :
1.BO Client : client machine calls BOMAIN.key on it's local drive, that sends info to BO Server's BOMAIN.key, validates it, then checks it into Repository, after repository validation user can access the BO services.
2.WebI : user logs into WebI using InfoView from web-browser, it talks to the WebI Web server, web server's BOMAIN.key checks the privilages of that user, send info to BO server's BOMAIN.key, that validates the info & forwards to Repository, if it validates the info, gives access to the universe & underlying dabase.