Probably the biggest difference is how many applications and how it goes on/comes off. Liquid is pretty easy to spread quickly from my experience, but a paste will likely go more applications. I do prefer liquid though.
There are two benefits to a liquid wax. One is that they generally contain more solvents than a paste wax due to the amount needed to thin out the carnauba. Carnauba in it's raw form is hard as a rock. Paste waxes hardly have any solvent in them while liquids have more. Those solvents can help clean the paint. The downside is that liquid waxes are rarely layerable. One layer would remove the other layer basically.
The other benefit of a liquid wax is that they generally have more filler product in them than a paste wax. Fillers are nice because they hide some of your swirls that you haven't polished out yet. Fillers are bad because they stain your trim. Just be careful with the trim and you won't have a problem.
Paste waxes are nice because they generally don't stain trim. They are also sometimes wetter looking due to higher oil content. That can be bad because more oil means more dust attraction. However there are also fewer solvents which means more carnauba and more durability. Side by side a paste wax will last longer than a liquid wax because of the higher carnauba content.
So there are pros and cons to either side. On one hand you can use a liquid wax that fills swirls and stains your trim while not being as durable, and then on the other hand you could use a paste wax that doesn't stain trim and is more durable while being slower to apply by hand and not filling swirls as well. It just depends on what you are looking for in you wax. I use them both depending on the color and shape of the car I am working on, so I really don't have a preference.