Generally laptops as they are more mobile and thus can be brought to meetings, when conferencing with a co-worker in their office, when holding a training in another location, etc. It depends on a lot on your needs. At my seasonal supervisor job which I work during the summer, we only have desktops for the supervisors and I often find myself wishing it was a laptop - or that our department had at least one. But I also understand they don't want to purchase all new PCs plus deal with the possibility of laptops going missing.
I like the versatility of a laptop. I prefer to have an external monitor because they tend to be larger. For me personally, at work I have a laptop and I also have a monitor and use it as an extension of my desktop giving me two screens to work with.
Desktop for sure. I like to be able to have everything I need to have open open, and it can be a little messy to have that done on a laptop. It's possible, but I guess I just don't like the set up. I don't mind using a laptop though since it's portable and I can take my work with me on the go.
At work, I prefer to have a beefy laptop hooked up to a couple monitors. That way, you can pick it up and take it somewhere if you need to, but it still has the function of a desktop.