Wow people sure don't like Sharla. I actually played as her for most of the game. I thought she did a better job keeping people alive when I was controlling her.
Sharla's biggest issues....are her breasts. *ker-bitchslapped*
Ehem. Sharla's biggest problem is the fact that she really only has one role to play unlike everybody else in that she's a support bot first and foremost (anti-air and early ether based damage seem to be her other uses, both of which aren't really game changing). Unfortunately, this means that she's not really that good at contributing to combat which means that what she's really accomplishing is dragging out fights. Its not really so bad at first since Shulk and eventually Melia and Riki are the only other characters who gain skills that can heal others and theirs consist of one option that doesn't do a lot at first. But then things like skills that enable healing after performing chain attacks or after scoring critical hits, or gems that heal when using arts or auras start to show up, and given how fast attacking or pulling out arts can be once they've been upgraded a fair amount, a lot of healing can be done automatically, and by then the aforementioned alternatives can cover the spread by themselves (not to mention that their healing art has probably been powered up by leveling and through skills). And then there's the fact that healing arts generate a ton of aggro (and though I was able to turn my endgame Sharla into a bigger physical tank than Reyn, its not a very common or practical solution), and the fact that other characters are just better at handling aggro.
But what's really damning to her is her difficulty in participating in a chain attack. She's the only character who can't use her talent art as a wildcard in raising/maintaining combos and her pallet is going to be dominated by blue arts with only the one red art (Headshot) which other characters generally get only one or two blue arts and several red arts (Melia's the only exception to this since her summons are blue but her talent art alone more than makes up for it). The big thing about chain attacks is that with the max combo multiplier you will get amazing damage out of your arts, i.e. you can turn Melia's Railgun into a Wave Motion Gun, any of Riki's numerous DOTs into corrosive acid towards even the most inflated HP bars (due to the wonky way DOTs apply the combo multiplier), or Seven's storm of swords into a buzzsaw of doom (not that the help is needed), among other things, but the most Sharla could do is soup up her Headshot or Thunder Bullet arts or heal thousands of HP to the entire party despite the cap being 9999 HP (which most aren't going to hit without gem/skill support).
The tl;dr is that she's useful early on when you can't pull off all of these shenanigans but eventually gems, skills, and chain attacks will tank the use of her contributions. Of course most of this doesn't really come up much since you'll generally be overleveled but UMs and the postgame will probably want to see her warming the bench.
As for Shulk, he really depends on the player and how well his Monado arts have been upgraded. Early on you're stuck with him and probably regulated him to AI use (which handles him fairly well). Then he's usually the first to get benched to make way for the dapper hero himself who easily outshines his predecessors due to his high agility and his arts being easy auras and simple combos. And he kinda starts falling behind until the end of the Eyrth Sea region where he finally gets access to three weapon gem slots and he no longer has to worry about the one or two fights where he's nigh onto useless in due to the Monado's friendly fire option being turned off. Then you hit Sword Valley and suddenly Shulk gets to have a field day while everybody else slowly converts to effective anti-mechon weaponry. By the time you leave mechon country Shulk should have all the AP needed to make his Monado arts really effective. His big niche outside of always anti-mechon is his ability to negate or mitigate incoming attacks and is the best guy to have on hand when dealing with vision tags, and his other niche being his positioning based arts.