I'm probably not the best one for this, but I'll give it a shot.
HP steels tend to be smaller in size, weight less, and have more negative bouyancy than an Aluminum tank of the same size. That takes a load off your back and belt! There draw back is that unless you have a place that can fill them to their rated pressure, you loose a good bit of air. For example, a Catalina AL80 holds 77.4cf of air when filled to 3000PSI, a Pressed Steel HP80 holds 82.1cf when filled to 3500PSI but only 70.4cf when filled to 3000PSI. So if you get a short fill, it has more effect. Also with HP steels you have to use a DIN fitting vs Yoke. That's not a bad thing, but since most rentals that you'd use on vacations would be Yoke, you'd have to either afix an adapter or have another reg with a Yoke fitting. Some people don't like the adapters and that's one of the things my wife will have to see for herself before making a final decision.
LP steels tend to be heavier, larger, and have less negative bouyancy than HP steels but more than AL tanks. They also have a lower pressure rating (usually 2400PSI + 10%, making it 2640PSI) that can be filled to capacity almost anywhere. And in alot of cases "overfilled" to give you more air for the same rated volume than HP or AL. For instance, compared to a HP80s 82.1cf @ 3500PSI and an AL80s 77.4cf @ 3000, the LP80 would have 91.6cf @ 3000PSI. Course at the same time it would be overfilled by 360PSI. The fact that they have more cf of air per PSI is what makes them so popular for cave divers. They also tend to be Yoke, with some exceptions, espeacially for cavers.
AL aluminum tanks tend to be heavier than and larger than HPs, but smaller and lighter than LPs, while at the same time have positive bouyancy, (with a few exceptions) when empty, compared to an HP or LP's negative bouyancy. But they are the most common found in the US and are usually always Yoke.