There are some games that are only available on tablets. The main ones for me are Jubeat and Reflecbeat, which are Bemani games that I have zero chance of playing in an arcade. They go with the song pack architecture, which I find to be annoying; in general I might like one or two songs in a pack, but I have to buy the entire pack and get other songs I have no interest in playing.
What I don't like about tablets is that getting information off of a tablet is often difficult or non-intuitive. I am used to being able to transfer files on a flash drive or LAN, but I am not sure how to go about it in a cloud environment. I am much more comfortable using a mouse than using touch screens; I feel they don't give the degree of control that I have come to expect from a computer. Typing on a tablet, especially a small one, is frustrating, and it's often very difficult to fix typos because it is nearly impossible to touch the right spot to put the cursor where you want it. I also don't like some websites default to the mobile version if you go to them on a tablet. In general, mobile websites have crippled functionality and are much more frustrating to deal with than the full website.
I also don't like Apple's stringent belief that its devices are so intuitive that they don't need to provide an instruction manual. We've had to do to the Apple store on a number of occasions because we had absolutely no idea how to do something (like when our toddler managed to mute the volume, which affected some apps but not others).