I assume you're making hard cheeses.
Presses tend to be much more user friendly, especially if you require a lot of pressure. Assume you're making a cheddar in a 6" mold and you want to use a modest 8 psi to press. If you only have a mold with a top, you would need to find a way to safely stack ~226 lbs on the top of the mold, then pray that it presses evenly and the cheese does not lean to one side causing the entire weight to topple over. This can be nerve-racking and even dangerous to pets, children, cabinets, flooring, yourself, etc.
Cheeses that require less pressure, like havarti or other semi-hard cheeses, wouldn't be quite as bad, but still, the risk of the whole setup falling and ruining a cheese would be enough to at least look into a simple press.
Personally, I have a spring type press from cheesemaking.com. Aside from being expensive, I know it has major drawbacks and limitations. Springs lose compression as the cheese is compacted, and I am limited to the amount of force that can be applied by springs alone. For the most part it works pretty well for me, though. After the initial pressing, I can pretty much leave it alone and not worry about it. I don't have to scour my apartment looking for "heavy things" that I can find, fill pots of water, or try to figure a way to get my mold centered under the computer desk (if I were pressing 4 cheeses at once, I could put one under each leg, but I would have to put the dresser on top to get enough weight
)