Even though beardies get bigger, I have to say they are FAR more easy and rewarding to care for than chameleons.
Chams are remarkable creatures, don't get me wrong I've had them myself, but they simply don't thrive well in captivity without precise conditions. They stress so easily. It just takes so much more work to keep them happy and healthy, and IMO isn't nearly as rewarding because they don't even want you to come near them except to feed them. I love chameleons as an animal, but I will probably never own one again.
Beardies on the other hand live longer, can do quite well in captivity when given the basic proper conditions, and allow you to handle them and actually sometimes seem to enjoy it.
So you can tell your step dad that even though chameleons are smaller, they aren't necessarily a better reptile to have for a pet. Tell him you want a pet you can hold and enjoy, not simply watch from a distance like an animal in a zoo. You can have an amazing, beautiful, friendly reptile with a unique personality that you can hold and show off, or you can have an amazing, beautiful, cranky reptile that would just assume you never look at it or come near it unless it's feeding time.
They really don't take up that much more space than a chameleon anyways. We're talking maybe a couple square feet of enclosure space, at most. 
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Amanda
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2.0 bearded dragons (Ocho / Domo-kun)
0.1 kingsnake (Rio)
1.0 ferret (Playstation)
1.0 cat (Wally)
0.1 dog (Tima)