This is the short version... I don't think the finished effect differs any. I can create the exact same curl when using either. I think straighteners have a slight degree of more flexibility in terms of the style of curl you can create but that's about it. If you just want straightforward curls, then either will be fine. Using the straighteners, I have managed to crisp my earlobe on more than one occasion. Using the wand, I have given myself a rather attractive 2 inch burn down my cheek. Also, with the wand, it's likely you'll be provided with a teflon glove - make sure you wear it on the hand you're holding the hair with and not the hand you're holding the wand with...
I use an AMIKA curling wand, which cost about £120 and my straighteners are SHE which cost about £20-£25. I don't need expensive straighteners, I have the straightest hair imaginable, I just use them for curling. They are both ceramic.
This is the side I curled using the wand.
This is the side I curled using the straighteners.
This is them both, helpfully labelled using my amateur Microsoft Paint skillz