Amir Taaki wants to bring complete anonymity to Bitcoin. First he has to demonstrate it on other blockchains. The SC developers can demonstrate it on an altcoin and if it works, then Bitcoin can adopt it. If they come up with a two-way peg that works, then the trade-off for whatever benefit the SC offers may be worth some sacrifice, like security or functionality. It's unlikely it can be more secure than Bitcoin AND have other benefits. If they did, then just hard fork Bitcoin.
One way in which a side-chain would not be identical to bitcoin is it has different features. Unless we have provable security the added complexity would tend to make a side-chain less secure. (And thats a reason for side-chains .. so that people can get access to more features without exposing other people to the risks relating to their feature).
For now there are also security tradeoffs in the 2wp mechanism, so that is another source of difference.
But in the future, if for example snarks or some other innovation becomes a proven secure cryptographic construct, then we can have security-equal sidechains (and security-equal smart-phones). And then it may be possible to have a more secure side-chain: make a simplified side-chain that doesnt include bitcoin-script, p2sh, etc ie strips a bunch of stuff for pure cold storage. Of course you also have the incentive compatibility issue, however over time the difference erodes as volume & hence fees increase and reward decreases as we get through more halvings.
Adam