I'm pretty sure that any calculation saying Lasgun is equivalent of .22LR went wrong somewhere, presumably in taking any tabletop numbers as a base. Roleplaying ones are eh, but tabletop very much doesn't make sense. As far as regular ammunition goes, you will probably want to look at Stubbers rather than Autoguns. There is some different tries to classify what are the differences, most notable being "Autoguns are caseless", which generally speaking works, but I don't think that's a defining feature of ALL of them, and that in terms of WH40k some of guns may be called this interchangeably. In the end I just guess the main difference is that Autoguns are generally the higher level type of guns, which usually involves them being caseless, maybe with some fancy shit like recoil mitigation, burst fires, maybe even targeting systems, but also presumably firing better projectiles, while stub guns are literally equivalents of many modern day guns (I am pretty sure some PDF world in WH40k has a heavy stubber lying around that still has something around the lines of "Normandy, Korea, Vietnam, Iraq, Mars" scratched onto it), and I am pretty sure there are references to actual honest-to-God-Emperor 1911s and Thompsons. It should also be noted that Imperial Guard armour should, in general, be actually really good, compared to what we have right now, being essentially the same in terms of how it works (+heat dissipating shit, I guess) except with way better materials.
Anyhow, regarding the Lasguns, I believe their pure killing power is on par with good autoguns, which should be "at least" as powerful as modern day assault rifles, but the Lasgun shots also carry much higher amount of pain and shock for exposed flesh, due to essentially exploding a chunk of someone's body with energy, cauterization or not be damned, which is also why they're comparatively a bit more destructive when it comes to solid materials that aren't particularly good at fast energy absorption.
I'd also contest various claims that Imperial vehicles and in general, all of stuff is bad, because while sure, GW often seems to have absolutely no fucking idea what they're writing and they're giving things like Land Raiders effective armour equivalent of a sheet of metal, but eh, I guess some of it can be bullshited away as materials from the future.
Also, yeah, Battlefleet Gothic. I am a bit sad it involves Nu-Lore, but I guess that's the next logical step. It seems to be very much like previous game, except maybe this time not so... unfinished even after few months (I liked the first one a lot, but I couldn't help but feel that what I'm essentially playing is more of a advanced proof of concept rather than complete game). I really like Imperial Navy, despite them being the unsung asshole heroes of Imperium (say what you want about captains not giving ground support, the pilots of smaller craft are pretty kick-ass), so I have it bought already, which I might regret, but oh well. The only problem is that I have entire tommorow (today, actually) busy, so I'm considering tactical sickness.