By a slide-in you're probably referring to a range-top. Rangetops are generally more expensive than drop-ins but you get a bunch of advantages. The knobs are on the front of the range-top so you get a larger area for cooking and usually more high-power burners.

Thanks that may help me look them up easier!

some manufacturers refer to their rangetops as cooktops or professional cooktops which makes the issue a little more confusing.

I agree with Weissman that sometimes manufacturers call rangetops cooktops, but most of the time a "rangetop" means, well, how it sounds, like the top part of the range minus the oven, with the knobs on the front.

Other differences - typically rangetops have each burner the same btu's, while cooktops have different btu's on different burners, and also sometimes different size/diameter burners. This is neither an advantage nor disadvantage; it's a matter of personal cooking style. Some people like a dedicated burner for e.g. simmering or e.g. high-power btu's. Other people like all the burners the same because they don't have to think about shifting pots around onto different burners depending on whether they want a high boil or low simmer. However, if all your burners are the same size and btu's, you better make sure you have a high-quality machine that will be able to simmer or high-power boil on each burner and do that regardless of what size pot/pan you have (Wolf rangetops come to mind).

Another difference is aesthetics. People perceive the rangetop look as more "industrial kitchen", while the drop-in cooktop is sleeker. Again, no right or wrong choice, just a matter of taste.

Space considerations - I would think that the rangetop will need more space in your cabinet height-wise. I.e. you may not be able to fit as many drawers under a rangetop as you would a drop-in cooktop.