I'm 1/2 & 1/2 on this.  I used the DM feature on Twitter for quite a while and the messenger on FB.  So I've seen it both ways.  Multiple tabs tends to crowd up a page, especially when you have multiple group chats going on.  I'd rather see it as it is, I tended to use Twitter's DM more because it was a chronological list, most recent at the top, that I could quickly reference for who I wanted and my page stayed clear otherwise.