I don't know much about this, but I think CounterParty isn't a side chain. It is using Bitcoins blockchain. It is basically a platform running on Bitcoin.
A sidechain is really a different chain that at times is locked into the Bitcoin blockchain, that basically the two chains interact with each other.
At least that is the way I understand it.
Back to the OP's question, which one is better a platform built on a sidechain or a platform built on top of the bitcoin code?
Well..... Counterparty has the first mover advantage, and since there isn't even a single side chain running in real life, CounterParty is clearly better.
This speaks to the fact that it is much easier to build on Bitcoin than it is to connect to the side. IF and thats a pretty big IF, sidechains are implemented they could in theory do more than CounterParty is doing now.
Then again, by that time CounterParty might evolve to also have new functions. That is what is going on right now where CounterParty and Overstock have teamed up to build an entirely new product called Mercedi.
Thanks for clarifying that!