Can you drag an attachment from your file system and into a message in Outlook Web Access (I have not tried). Can you do that in with FireFox and Chrome?

Last time I used OWA, a long time ago, it was IE only for any kind of usable experience. That meant that it used a bunch of non-standard MS only extensions to support that functionality. In such a case, your example is meaningless. If this has improved since I used it, then you are right.

For a good web mail app I'd point to Yahoo mail which works with all browsers I have tried.