That’s tricky to tell but I get the odd impression that while Barry Allen and Tim Drake (to some extent) don’t lack personalities, the problem is what keeps them from developing real personalities’s that writers keep projecting a somewhat idealised version of their target demographics onto them. People have been writing semi-idealised author surrogates for years.
The major difference is that Barry Allen and Tim Drake have been written by different authors over time that it’s that hard giving them a definitive direction and personality. Let one a personality outside of the idealised target audience. Self-insert characters are inevitable as many written works are autobiographical to some extent.
Though I think real Canon Sues are more likely to be supporting characters that resemble a certain target demographic if Arrow’s Felicity Smoak’s any indication. Tim Drake fits squarely into my take on Canon Sues. Barry Allen deviates it somewhat by being the main character.
Canon Sues are paradoxical in that they’re supposed to be normal even though they only closely resemble the target audience and it’s not that they’re flawless but there aren’t that many lasting or profound consequences for what they do. JJBA’s Rohan Kishibe (and Josuke to some extent) have consequences for what they do.
Both of them are based on the author to varying degrees. Rohan loses his cool and literally writes on peoples’ faces whilst Josuke loses his cool from being taunted and nearly beat Rohan to death as well as things going awry whenever his familiar tries to fix them when Josuke himself gets pissed.
That isn’t to say there isn’t any for Marvel’s Kitty Pryde and DC’s Tim Drake and Barry Allen. With Barry Allen, especially with him trying to undo his parent’s death there are consequences but the setup’s treated as nothing more than a plot device. Kitty Pryde’s got a bad temper but it seems whatever flaws she has don’t have profound or lasting consequences.
In fact they’re immediately undone though I could be misremembering about JJBA. But the point here’s that author surrogates can always evade being/becoming Canon Sues. Rohan Kishibe being a Mary Sue’s up to anybody’s guess but I think the real defining factor for a true Canon Sue’s being readily appropriately by fans.
Authorial surrogates usually don’t count much as many fictions do have semi-autobiographical elements. (Kishibe’s in a grey area.) True Canon Sues by contrast have a lot of similarities with target demographics, especially if they’re specific ones at that if Buffy’s Willow’s any indication. That got averted in canon where Willow becomes evil.
Tim Drake, Kitty Pryde and Felicity Smoak are way better examples of Canon Sues in that they not only have a lot of similarities with niche audiences but also where either writers have come to pander to them a lot (Felicity, Tim and Kitty to some extent) or where fans get to write about them (James Tynion to Tim, Joss Whedon to Kitty).
Barry Allen’s in a grey area where he’s somewhat idealised version of his target niche (superhero nerds) and got written by them, especially Geoff Johns. Yet he has flaws like tardiness and there are profound consequences for whenever he does try to undo his parent’s murder. Often messing up timelines.
I’ve come to regard both Barry Allen and Rohan Kishibe as ‘Grey Area Sues’ where they’re both semi-idealised versions of both audience and author(s) yet have also have profound consequences for what they do (Rohan gets beaten up by Josuke for taunting him) though with Barry, it comes off as a bit of a plot device at times.