I feel, rather to my amazement, that the three live-action shows (haven't got around to the McCabe misadventures yet :) ) have managed to set and maintain surprisingly consistent 'diverse yet compatible' tones. They don't feel as is they're treading on one another's toes, lifting plots wholesale and running them once through the spin cycle for names, which in my experience can easily occur in linked series.
However, probably the things I'm enjoying most about each show therefore differ quite extensively. With 'Flash' it is the endless linking, to the comics, to worlds seen and partially experienced, to futures that may or may not have a gravitational attraction of their own - and the clear example is the glacial (speedwise) petrification of Caitlyn, the stripping away of her touchstones and pole stars. If she does (within the show) make it to KF we will C (sorry, couldn't resist) a trailing comet-like tail of her evolution back down the line.
As for Arrow, whilst on occasion it feel as if (with the exception of the season's Big Bad) whatever doesn't get resolved in forty-two minutes is liable to be shelved, the staccato, for me at least, helps to ground the series, since elaborate plans, on the part of our heroes anyway, rarely are allowed to come to fruition. As John Lennon famously observed, "Life is what happens to you while you're making other plans". Knowing the comics as I do, I also love the lingering link between Ollie and Laurel, even though I think (within the TV context) Felicity is a fantastic, and indeed better, choice for him, for now.
When it comes to LoT, perhaps six episodes is jumping the gun to comment, but they seem to me to have hurdled the whole paradox/timelines/own grandfather issues bundle by sweeping it neatly off to the edge of frame, acknowledged, but no one's trying to unwrap it. With true freedom to roam, it's hard to argue that they get lucky all the time/too much since almost by definition they must be homing in on certain criteria and requirements, and the requisite implausible somehow no longer endangers disbelief. Obviously, if one feels the premise is flawed, the whole structure collapses under its own weight, but that's true of any 'fantastic' tale. The constantly shifting dynamic of people each with their own, not always compatible, agenda, makes for endless opportunities for wonderful, theatre-like, intense short scenes, and the feeling that roles are by no means fixed, any more than destinies - or, indeed, personalities. Niches are developing, but they don't have an aura of inflexibility, a sense that this is the comprehensive definition of the individual within.