Shirley it's just latent heat and thermal mass of something that's approximately water, so for an equivalent mass performance isn't likely to be very different[1]. I'd choose whatever's a convenient shape (IME the limiting factor is finding room for it in the freezer before use) and is reasonably durable.
Gel packs that remain flexible are useful for injuries and smaller coolbags.
FWIW we've got some of those rigid plastic packs with liquid that freezes solid (presumably water with a bit of glycol) in them, just like the ones my parents had in the 80s. They're about 20 years old and still work fine.
A useful trick is to make use of whatever other thermal mass you have to hand. Bringing a tin of beans? Cool it down in the fridge and pack it in the coolbox so it can help keep the milk cold until you use it.
The real challenge is what you do on the second day, unless you're at the sort of campsite that provides freezing facilities. Usually that's buying a bag of ice cubes from a supermarket, and the coolbox turning into a poolbox as it melts (not sure how well that works with a bag). Otherwise you're into active refrigeration, which is the realm of ammonia-cycle gas fridges or electric hookups. Our coolbox has a peltier thing in the lid, which is sufficient for keeping it at reasonable fridge temperatures indefinitely, iff you can feed it the 100W or so it requires.
[1] Obviously an ice pack that was less effective at transferring heat would stay cool for longer, but then you're getting less cooling from it. In my mind, if you're going to insulate something, it's better if it's the outside of the coolbox.