I like to host. I enjoy it … but I think the underlying real reason is that I like to have more control over the space I am in.
Visit. Hosting is too much work, plus I’m paranoid that people are judging my standards of cleanliness, they don’t like my decor, maybe my house smells funny and I have no idea, etc. I also like the option of getting up and leaving when I feel the visit has run its course, rather than trying to politely usher people out of my house (which is impossible to do).
Cleaning sucks. But more importantly, it’s easier to get up and leave someone else’s house when I’m done than to try to kick someone out of my own home. I will cheerfully visit every time.
This is interesting. I don’t know what I’d expected the results to be, but it does surprise me.
I’m a prefer-to-host person, and I’ve always felt slightly guilty about making my friends come to see me instead of going to visit them - I’d sort of assumed that traveling was more of a burden than seems to be indicated here, and that it would be a landslide toward hosting. Instead, it seems to be somewhat evenly balanced.
Go fig.
Definitely guest. I’m such a lousy host…also, I’m assuming food is free, and the hosts do not mind, since we’re talking druthers. What’s not to love?
I would prefer to host. I have a kegerator, my house is mostly always clean, I love to cook and cook for others and have a cozy yard with a chiminea.
C’mon over!
I’m a few blocks east of Jupiter, could ya give me directions? 
This. I would put crocodiles and/or alligators, as well as Parana, in the moat.
I do not drink, so no worries about me not getting home safe. I will gladly supply the food, you cook. I can, but it is not great. If my host drinks, it is OK since they are already home.
I have a friend that we do this exactly for the drinking reason. He is happy with this arrangement.
I chose guest. There are four reasons I can think of off the top of my head:
(1) I do enjoy socializing, but I can get tired of being around other people very suddenly. It is easier to excuse myself and leave than it is to tell my guests that they need to leave now.
(2) TV watching can be a good group activity, but is almost never the way I want to spend my time when I’m alone. By being a guest in someone else’s house, I can avoid having to pay for cable at my own place.
(3) I’ve converted my living room into a workout space, and combined my dining room and living room into a single tiny space. It works great for my needs, but makes for an awkward hosting experience.
(4) I don’t like cooking, and if you’re a guest you’re usually not expected to cook.
Visit. I already sort of have this setup, except it’s further than 45min away. I’m isolated in this city and there’s more reason for me to travel to them instead of them coming to me. It works out well! My friend is such a mama type and loves cooking for people. Plus, since I usually retire earlier than everyone else, it’s an easy exist. 
I voted “prefer to host” but my vote might be shaded by my current reality.
For the first 10 years of so of our marriage our house was the default gathering place for all social activity. We were the only ones with kids so everyone came to us.
Now my kids are grown and gone and my friends have young kids so I’m always visiting.
I’m very much looking forward to next May when we move into our house and one of our best friends moves into theirs - right next door. Will make a more balanced exchange of hosting/visiting much easier and with two of us in the same spot will again tilt the default location to our places.
I prefer to host but that’s because I’m a homebody and a control freak. I like to know exactly what will be served and I prefer my mode of entertaining (I prepare, you relax and enjoy) to my friends’ (we all help in the kitchen - whee!). And the selfish part is, I wouldn’t have to drive home at the end!