Comparing a successful fork to a runaway sidechain.
A chain fork, while painful, will succeed only if the fork is better than the original. A bitcoiner need only do nothing to join the fork.
A sidechain will either be less valuable and therefore be very small, or more valuable and therefore run away. A bitcoiner might be left behind, unless he converts to the sidechain in time.
I prefer a chain fork to a runaway sidechain.
Yes, chain fork = (Peter R's) spin off, though the latter carries a connotation of being done in a somewhat less chaotic fashion. As I said before, spin offs make a lot more sense than side chains as a way to (potentially) upgrade bitcoin. Even Adam's one-way pegs are better than side chains, but spin offs are better than one way pegs.
But Blockstream's two-way pegged side chains don't runaway from your BTC value. Thus they are best, because they are not all-or-nothing choices, you can go back and forth, and your BTC value is protected.
Pegging two different, however slightly, money types together is a problem in theory and practice. As long as they are different, they will have different value. If the value is smaller, they will be converted to bitcoins. If the value is larger, they will be converted to sidecoins.
When a fiat system goes bust, a new one is created, and it is quite common to peg the value to for instance the dollar. This is to try to give people a reason to trust the new money. The reason to have local money at all, is to get the seigniorage, which otherwise would be wasted to another government. To peg the value, you need an institution to be the guarantor, that means a kind of bank with reserves in the other money type. In practice, exact pegging is not possible, because there will be leakage of value to speculants and money exchange services. Therefore there will be a band, where the value will be pegged to somewhere between the upper and lower limits. Even better, the exact limits are secret, to avoid speculation near the edge. This can go on for a while, until they have created too much (sometimes too little), the peg breaks and is set to another value.
If there is a mathematical peg defined by protocol and secured by the blockchain, the difference in value will have to escape somehow, and that is either the coins disappear if they are worth less than bitcoin, otherwise all bitcoins will be converted to sidecoins. It is not rocket science.