I had both and I used both.
The slingadapter only works with the Dish app and has pretty good intregration with the Guide and DVR listings in a native app/web interface format whether on a mobile phone or from the web. The problem I always had was randomly, the Dish Online service would just stop talking to my receivers effectively cutting me off. From what I understand, that is still an issue though I can't confirm because I no longer have the Slingadapter. It is easy to install with a single USB plug and that enables full control of the receive through the app/web.
The Slingbox OTOH is a seperate hardware device with seperate software that effecitvely operates as if you were sitting in front of the TV at home with the remote. So what you see on screen [software] is what is on the TV screen if that makes sense. Because it is seperate, you have a seperate power, network cable and a/v cable to deal with and it uses an IR transmitter cable to give you IR remote control capability.
The last annoyance is they are not interoperable! If you have a slingbox, you must use the full slingplayer app, the Dish app will not work and vice versa, if you have a slingadapter, you must use the dish app as the singplayer app wont work. To me that is the stupiest thing they did but I digress....
The cost is also an issue: The slingadapter is $50 period. I currently have the Slingbox Solo (formerly had a Slingbox pro (2007-2012) before it died after 5 years of use that I gave $199 for and the original slingbox (2005-2006) before that that was $149). I paid $99 on sale for the current Slingbox Solo and then about $30 for the Slingplayer app way back when on blackberry and then $15 for the current iphone app.
As far as preference, I no longer have a slingadapter if that tells you anything
Overall, I got tired of the Dish App/Dish Online site disconnecting from my receivers and lost all tolerance for messing with it. With the Slingbox/Slingplayer, when I start it up, it connects and it's always stable.
Oh and contrary to what someone said earlier, if you connect the component inputs to the Slingbox - HBO will still work as the HDCP checking is only enabled for the HDMI connection. I have my Hopper connected directly to the TV using HDMI and the component cables from the hopper plugging into my Slingbox.