I'm about to test both...my results after two days:
You can switch between both very easily...
Mightytext has a very nice desktop user interface. All works smooth so far. I'm just not able to send MMS with pictures from my desktop. On the smartphone you get only a screen for adjust some settings but all SMS and MMS will be done by your standard app, that's also great for me, so I can select the best userinterface I like.
There are two pages to login for handcent. One is for the user account and one is for the SMS and MMS userinterface. I first only found the page for the account. There is no link button to switch between them, that's really bad. But after searching in the web I found everything and it works now fine. The app on my smartphone (Samsung Galaxy Note 4) looks very, very good and works in all aspects very well but is not very fast, no it's really not fast. Handcent replaces your standard SMS app, that's not bad because the user interface is really very well made and surprisingly the language is very well translated to German. Super.
You have to enable the Handcent anywhere service on the phone before you can use the Desktop interface. This is a little bit more complicated as on Mightytext but possibly also more secure...
I'm not at the end of my tests. I like the Userinterface of Mightytext for the desktop and the way of implementation on the smartphone but I'm dissapointed that MMS can't be initiated on the desktop (sync works fine also for MMS).
So currently only Handcent works on the desktop and the smartphone and I think I will go with Handcent...