The problem with the Mr. Saturn is as soon as we see it, we're going straight for the air, and shielding a lot less on the ground. Often, Jigglypuff will already be in the air and will have enough time to notice the Mr. Saturn.I think its Turnips that gives Peach that slight advantage.
Also, even the thought of getting being able to kill her in one hit with Mr. Saturn (doesn't even matter if she can avoid it, the possibility is still there) also gives her an advantage in my book.
That could be applied to Bomb pulling as well, but they're much rarer.
Bombombs on the other hand is ****. My only answer to that is to get as high up as I can so I can see the bombomb coming and avoiding it. Energy Sword outspaces us pretty hard.
I'd call the matchup 50:50 until Peach pulls out something like an Energy Sword or a Bombomb, then it leans more towards 55:45 Peaches favor (Assuming the bombomb collides).