[NOTE: "The Battle of Vicksburg, MS" was more-accurately described as a whole series of skirmishes & battles, ending with a notable siege.]
Oof, I guess this might make for an upsetting or somewhat controversial post, but I figured it best to stick to the facts rather than omit significant details. Or worse yet, try to whitewash the whole affair. Now, while it's true that the classic, Belgian-produced Les tuniques Bleues is 'merely a comic book series,' there's just no escaping that it directly depicts the outrageously awful American Civil War, even while portraying it in an innocent, cartoony way.

Bottom half of the page above. (source: Imgur)
So, yeah... across the past few centuries, I think you'd be hard-pressed to find a more awful conflict than the ACW, unless it might be the two World Wars. It was fought over a dreadful premise-- that of the industrialised, generally Northern States & the Federal Government fighting to prevent a group of generally Southern States from breaking away, which they did expressly for the purposes of maintaining the practice of slavery, which of course was deeply integrated in to their culture and economies.

The first couple books. (source: BDT)
I think a big part of what made the whole affair so awful is that the US had still not abolished slavery by the war's start (~1860), whilst most other major nations had already done so years before... some as early as the 1500's. So the US was in an arguably terribly embarrassing global position at the time, especially being nominally the very first modern democracy, with some famous, documented statements loudly trumpeting the fundamental rights of man(!) <TUSDoI> <TUSBoR>

The two leads, Sgt. Chesterfield
and Cpl. Blutch. (source: WP)
Even worse, here you had a regional peoples across a network of States who were largely not embarrassed about slavery, who very much wanted to continue the practice as long as possible. Of course, publicly they tended to avoid saying that in a leading-cause sense, instead talking about "States Rights," which became something of their self-righteous, strangely-hollow battle cry. Dig slightly deeper in to most of their official grievance & separation documents, however, and it became very clear what they were actually after.

Another day, another battle (source: BDT)
Another dreadful, different aspect of the war is that it resulted in the highest number of casualties for any war involving the United States. It's estimated that 620,000 to 750,000 soldiers died in the conflict, surpassing the combined casualties of all other American wars, including both WW's. Much of those totals were specifically due to disease (such as terrible prison conditions, especially in the South), as well as new, deadlier weaponry combined with outdated military tactics, such as traditional, massed formations.

A T1 page (1972) vs. a T68 page (2024) page
As with most (or all?) civil wars, the conflict also tore the country apart, not just pitting family members, colleagues and dear friends against each other, but creating (or perhaps "highlighting") a deep, fundamental divide between various ideologies in The States, which arguably has been nothing but magnified over time, persisting and even thriving today, with misinformation all too common a thread.
Anyway, much more can and already has been said about the war itself, so let's move on to some specifics about what this series is actually like:

Crossing a ford. (source: "time-to-collect")
Well, I've read a couple albums now, and so far have found it more or less to be light adventure combined with silly humour. The pairing of Chesterfield & Blutch function as something of a classic, comedy duo formula, with the Sgt. in the 'stiff-but-responsible' role, and the Cpl. in the 'cowardly-but-unpredictably-creative' role. Likely, you can easily name half a dozen counterpart examples of your own across any number of genres, eh? I suppose my point here is that this is not a series about character development, but moreso about Vaudevillian-esque characters doing their thing amidst a stressful, super-dangerous conflict.
Now, as for the troubling background themes of the ACW, they're not tackled directly too much, rendering this fairly upper-middle-tier BD fare on the whole, I'd say. Somewhere in the ballpark of "Spirou," perhaps, with the characters being a little less memorable, and far less free-ranging. After all-- just about every setting in the series occurs in the Eastern and Midwest USA, during the tight, four-year timeframe of the civil war.
Remarkably, the series spans well over fifty years now in total publishing time, across a whopping 68 main books and ~10 tomes of special-content editions.
Right, so-- hopefully I'll have more later on specific Bluecoats adventures. And BTW, one last thing I wanted to do is to note some other titles people may want to check out:

Similar works. (source: Imgur)
BD has long tackled the ACW through both humor and gravitas. The Bluecoats is perhaps the flagship series; but less comedic works such as Mac Coy, Virginia, Le Chariot de Thespis* and La sale Guerre de Sécession explore more complex themes and perspectives, all while delivering strong visuals anchored in historical settings. --GPT with JE edits
Ooh, AND HEY-- this posting just so happens to mark the precise, two-year anniversary of this sub/community. It's not exactly what I'd intended to mark the occasion with, but ah well. :S More on the anniversary later!
Answering the real questions!