Barst vs. Sedgar comes down to the worth of earlier chapters, because Sedgar eventually beats Barst forever in martial stats, at least in the scenario where they are both Heroes (the best promoted class for both, I think).
In my playthrough, which is at Ch. 15, Sedgar is still losing to Barst offensively from a mt perspective. He has no Hand Axe access yet, and he's reliant on an Iron Axe forged to Silver Axe prowess just to tiegame with what Barst can do with plain Steel. Defensively, Sedgar is superior only in DEF, since they have about the same HP and RES. This is an advantage for him, but it's not as big as you might think, since Barst is basically getting 3-4HKO'ed at this point anyway.
Anyway, Barst has more headroom in his level ceiling, but he loses growths badly so the writing is on the wall, here. Within about 4-6 levels, Sedgar will begin to surpass him in STR, he'll be faster, have good 1-2 range with Hand Axes (this will happen very soon), and lack of access to Hauteclere and Silver won't be a big deal due to the presence of forged E and D-rank Axes. About the only thing that Barst will retain is Hammer/Poleax access, but Sedgar won't care about taking counters and has the STR/SPD to largely brute-force his way regardless.
So this comparison is about the earlygame. I need to point out here that Barst doesn't know what it means to have a period of suck, because he's always one of your best units. He starts with D Axes, which is quite fortunate for him, since it allows immediate Hand/Devil Axe usage, and lets him skill up to C for Hammertime just when it's needed.
Sedgar doesn't even exist in Ch. 2-4, and might as well not exist in Ch. 5. You need to spend the next 3 chapters -- including the 6x Gaiden -- handling him gently and trying not to break him. You need to feed him EXP, pre-chewing enemies for him, because he's not good at getting it on his own. You have to be very careful not to over-extend him, as his durability is quite fragile at this point even as a General, and he's prone to getting crit-killed by everyone and their mother.
I'm not going to detail every little notch in Sedgar's growth chart -- partly because it's already detailed in my 2.0 log, and partly because it's PE and subject to RNG alterations -- but suffice it to say that Sedgar's training period must continue on a periodic basis until about Ch. 12 or 13 or so. Now, unlike his extremely early game, where he has to be babied, after about Ch. 8 or so he can handle himself and he's generally capable of doing something useful for the army.
However... Barst is basically one of your best units this entire time. He's fighting for MVP status, but he's fighting with Caeda for that title, not with Sedgar. By the time Sedgar actually starts to beat him, I expect that we're in Warp-skip territory, which is where Barst's durability doesn't even matter anymore.
I reserve the right to adjust my opinion as late game becomes reality instead of theory in this playthrough, but I don't see how Sedgar can possibly claim to be more vital for efficient play than Barst. This game is about 10 chapters too short for that.
