I'm 5'4", 125 pounds, and ski in northern Vermont at places like Stowe, and Jay peak. I want an all mountain twin that will do everything. Something that will make tight turns in the woods, carve nice on the groomers and hold an edge on ice, perform in the moguls, and I want something that will float on powder days. Ive done some research, and these two seem like what I'm looking for, although I'm open to any other suggestions. The only thing is I want to keep it under $400.
Line Sir Francis Bacon Shorty vs Sick day Shorty
Un-possible, no ski does everything well when 'everything' is that^^^ diverse. TANSTAAFL.
Sounds like the Sick Day Shorty might be a pretty good choice for what it sounds like you value most- ungroomed, softer snow performance in east coast trees. If edge hold on ice and groomer carving are more important, then maybe not... but still better than the SFB shorty. The SFB is a miss on too many of your parameters.
Money doesn't buy magic. Nothing is going to make a ski wide enough to float in powder feel fun on groomers, nothing that has a loose, surfy feel for wiggling through east coast trees and moguls will have excellent grip on eastern ice. It comes down to making informed compromises, a little honest self assessment about where you spend the most time and what characteristics you value most is key.
The Sick Day Shorty is probably a very good choice for the OP, it just isn't 'good' at groomers and 'ice' compared to ski which actually are good at skiing on groomers and ice. If skiing groomers and ice are more important, then there are skis that do that really well and are OK at skiing in the woods and have reasonable softer snow performance. Skis in the mid to high 80mm range would be a good place to look.