Sheik vs Luigi is definitely tough. Even BOSS LOST against Neo's Sheik as Luigi. Oh man, this MU is going to be something ludicrous like 80:20 Sheik's favor....
Really? Could you link to that game? I've mostly only really found Boss's games from S@X, IIRC, and I didn't get to see any sheik matchups. What few I did find of different players felt to be a mite lower level (i.e. were looking much closer to my own games rather than having more power shields than a lv9 CPU), so it's a bit hard to tell if they were playing at equal skill... though, I suppose that'd mean the inverse argument of purely analyzing Boss could be considered irrelevant as well, if he felt to just be playing significantly better. Though, only a very few games I saw quite felt like that.
Anywhos, but Bowser is definitely one I've seen a fair bit of as well as gotten to play fairly often, and I'm starting to get a bit of a picture of the matchup... To start with, be
very careful about low % fireballs and jabs, as they are uniquely unsafe whilst Bowsers at unflinchably low %'s. Starting a match with cyclone or a more tentative approach will keep you from fireballing into a free dash attack or jabbing just to get dropkicked for your trouble. In face, even later on, your fireball approaches can be zoned out occasionally by that flame breath, so I've found them to be a bit less reliable than usual-- that said, it's still handy for a bit of poke and covering your recovery, and you only need be
too worried if tempting flame breath with the lag of fireball or if he's sticking to low %'s. Speaking of his fire breath, be very careful about it when recovering-- stay calm and don't waste your second jump into it just to get gimped.
Beyond those nuisances, Bowser's main tools to look out for are the long range of his tilts (and even his jab), along with the fact that you can
never afford to be in landing/attack lag below him (or behind him) when he's airborne-- those drop aerials and drop kicks might be punishable, but they're a bit safer against Luigi than most due to our slow air speed, so the most we can generally follow up with is a cyclone unless they space it really poorly. On the ground, keep an eye out for the occasional whirling fortress, which can have some similar uses to our cyclone at times. You can consider quite a bit of his kit to be kill moves, but, luckily, he's also extremely east to combo. I can even manage the downthrow->Fair->Fair->downthrow->Fair->Fair combo on the 3ds against Bowser, and I've heard that he's quite vulnerable to the downthrow->diar chaingrab, as well-- those aside, do keep in mind that you'll need to space out Bowser's Fair, as it has a bit of range to it, and that our key advantage here is how easy Bowser is to prod out openings in for a solid combo or KO move. Downthrow->Nair/cyclone have been what I tend to use for taking Bowser out, myself, but up B can hit his lag after smashes, drop aerials, rolls, or
even his spotdodge... I mean, really, I'm not sure why, but Bowser's spotdodge feels remarkably unsafe. Speaking of defenses, though, shielding is, as per usual, the best defensive option we have. Be careful about shield damage, of course, but rolls and spotdodges are a bit more dangerous (as Bowser tends to require a playstyle of heavy reading to begin with, so he'll be looking for them as punish opportunities a lot more often). Luckily, Bowser's grab game isn't massively threatening, as he has little in way of combos or KO setups out of them (barring side B), so you can generally afford a couple of stray grabs far more than you could a single dropkick to the head after a poorly spaced roll.
But I've a nasty habit of being a bit too verbose, so let me try to summarize that...
Bowser feels to be at a slight disadvantage, overall. While he limits our options at most %'s, between unflinching fireball hits at low % and extreme killpower with rage at higher %, these are mitigated by Bowser being so easily comboed into middle %'s from a single grab or the like, and his power with rage is similarly gimped a bit by our surprisingly reliable KO potential against Bowser. Up B is almost BnB from as many openings as he's sure to provide. Cyclone, nair, and bair all work nicely as KO moves as well, of course, and Fair along strings so many free hits together due to Bowser's startup lag on his own aerials and his gigantic size. An even game in neutral, perhaps, as neither have much in way of safe approach to one another, but it feels like Luigi's going to find a far easier time keeping any advantageous game states he can sneak in a lot easier than Bowser-- of the two, Luigi just has far better options for a 'reset to neutral'. For Bowser to win, he'll need to force a lot more openings, as he has a harder time capitalizing on them than combo king Weegee might.
Hope that's of-help-- again, take my perspective with a grain of salt, as I've only been playing Luigi regularly for about two weeks now, with about 2-5 hours or so of play daily... other than that, I last played him to any real extent as a secondary or tertiary (been a while-- all I remember is so many Marth Fairs and screaming at tap-jumps...) in melee (because wavedash for miles...).