Thicker strings have more tension, mainly, and some other properties come about because GHS strings of that thickness are compound-wound.
56 would NOT be the 'next one down' - if you look at a seven-string pack, it'll go 10-13-17-26-36-46-56... but seven-string packs suck horribly. The 46 is already too light to 'match' the rest of the strings (E will be about two pounds of tension shy of the A) and the 56 is even farther (about 5 pounds shy of the A) - you should replace the 46 with a 49 and the 56 with something between 60 and 65 if you actually want to 'match' the A string. If you want to go past that, then go to 70. It seems like a very big jump, but keep in mind that low strings need larger size changes to be noticeable - anyone can tell the difference between a 9 and an 11, but compare a 46 to a 48 and you're getting nowhere fast with most. I figure that if you're going to go heavy, you're going fucking heavy... I tend to take things to extremes, as some around here notice on occasion.
EDIT: If you weren't already fairly familiar with string gauge changes, thicker strings result in 'thicker' tone, different harmonic response because of the increased tension, and better tuning stability. You can then get away with hitting them harder (because they won't go sharp on harder attacks) and thus get higher dynamic range and more versatility. END EDIT
Jeff
