The special detergents that are "baby-specific" are usually scent-free and have fewer ingredients that would be likely to irritate delicate skin. Some baby detergents have a soft scent that is very recognizable, at least in the United States, as a classic baby smell. This type of detergent is fine to use if that's what you like. Some parents find that these detergents don't do as well in removing tough stains, so you may need to use a good pre-treatment for satisfactory results.
A second category of laundry products to consider is scent-free detergents that are not baby-specific. If you have trouble getting clothes clean with the special baby detergents, these types of detergents may be a better choice. This may also be the best choice if you require a high-efficiency detergent, as you might find this variety more commonly available in that formula.
One advantage to choosing a regular, scent-free detergent is that it's easier to do the whole family's laundry without switching soaps. If you prefer a scent on your clothes after they're washed, though, you may not be happy with this type of detergent. If there is a family history of sensitive skin or scent/soap allergies, consider choosing this type of detergent right from the start, since baby may also have those sensitivities.
I prefer to make my own powdered laundry detergent that works for cloth diapers, baby clothes, and everyone else's laundry. This is pretty easy to do and is really cheap to make, plus you can customize your own version with essential oils if you like scented laundry.
One last choice is just to wash baby's clothes in a regular, scented laundry detergent. So long as your baby doesn't have any skin sensitivities or allergies to the scent, you don't have to buy a special detergent just for baby laundry. If you choose this route, be sure to watch baby's skin carefully to be sure he or she doesn't develop any rashes or reddened areas, and ask your pediatrician if you have any concerns about potential irritation from baby's clothes or the detergent.