Hi Jamesavery,
I can see there is a lot of love here for Zopim but let me tell you my experiences with both chat softwares Zopim &Livechat inc.
If there was one reason for choosing Livechatinc over Zopim it would be the degree in which you can easily customise the We are here and the Chat Online chat speech bubble.
I conducted a split test with a client of ours using both chat softwares to find out which chat software engaged and converted the client to initiate the chat function.
Because of the custom graphic that we used in Livechatinc we found that we had a massive 600% increase in user engagement.
The second big advantage with Livchatinc is the custom downloadable chat client interface which is just like having Skype in your system tray.
The reason for it being an advantage is that some chat sessions could potentially be missed with Zopim due to being browser based. Basically the chat notification is in the browser and could potentially be missed if youre working on a different browser or monitor.
My final reason would also be the ability to see what the visitor is writing prior to them submitting their message. So preparing the canned response or pushing them to a page with the information they are looking for is much more efficient.
Other than that its pretty much like for like on features!
Neither chat softwares come cheap but this link should ease the pain if you do become interested in Livechatinc:
http://www.appsumo.com/livechat-hot-promo/?rf=srch#overview