It is true that for market as a whole, laptops outsell desktops. Considering that business buy a lot of desktops, in the home market laptops are more like 75%.

Some advantages of desktops are reliability, and of course that many of them can add a better graphics card if you need it. Since they don't have to squeeze everything into a tiny space, reliable cooling is easy with a desktop compared to a laptop. If anything does fail, replacing most parts on a desktop can be done in a few minutes by someone with no special ability. Few laptops survive more than a few years, and repairs cost enough that buying a new laptop is usually the obvious choice.

I would choose a desktop on price for a certain level of specs, not brand - I've seen very good reliability from even the cheapest brands. One factor many people ignore is noise - some desktops are much louder than others, and although you can fix that by replacing fans, it can take some effort. So you might want to see what the reviews say for noise produced if that matters to you.

You can get a quad core in a slim case from Dell in an Inspiron 537s, which should be massive overkill for non-gaming performance. HP Pavilion Slimline s5250t or s5280t can also have quad-core, or the s5200z can be configured with AMD triple core.

However, along the lines of what I said above, slim desktop PCs are less reliable and often harder to repair than full size mini-towers. They use power supplies that may be harder to find, and have less air and space in the case so cooling is more of a problem. Many of them don't have slots or power available for good video cards.