You'd have better luck playing on a server made out of gingerbread cookies than over Brawl's internet.

Certainly, all characters have kill moves, but a number of characters have far more difficulty landing said killing moves in the middle of a fray. I main ZSS in Brawl, and she's an absolutely great character. The trouble with ZSS is that a good portion of her kill moves are difficult to work into a free for all brawl, most of them need a set up move like D-Smash first. She has side special, which works until it gets stale (which happens really quickly), and it's pretty much impossible to set up any sort of D-Smash combo when people around you are going nuts. So, in short, it's almost impossible to play ZSS and do well in a free for all time match, simply because her "killing" options are a bit more complex than someone like Ike who can kill easily in the middle of a crowd.

The difference with changing the mode is that it no longer becomes about who dishes out the killing move. Certainly, characters like ZSS are still at a disadvantage in an environment as crazy as that, but it's nowhere near as ridiculous a disadvantage.

And sure, you can switch characters, but personally I'd say that the mode that allows for any character, given he/she is played well, to have a chance to succeed is preferable.