The sword is pretty fun as well as the standout weapon, and I'd say Shadow Warrior easily has Doom beat in terms of melee combat, not even the berserker pack can compare. But pondering on your post a bit I still don't find the general combat design as well developed from my experiences.
My approach seems to blame, but for the bigger enemy types I would opt for maintaining distance and using guns, when it seems I should have gone for katana surgery. I tried picking up from a point in chapter 9 on Insane to just get more of a feel of my issues, and another thing I think that piles onto it is that you're often placed in arenas before you can continue. In Doom, levels were fairly open for you to backtrack through or even charge past encounters, but Shadow Warrior tends to lock you into an area where it will not allow you to do anything but fight until everything's dead. This leads to moments like the one where I just came across where I'm in a construction site, used up my remaining ammo on the grounded enemies that you're immediately presented, then leaving me with solely my katana as a group of flying types spawn in. Then I'm just kind of left clumsily doing the energy wave over and over again on enemies that don't really present a threat, but are overly numerous and are blocking my ability to progress for simply being there. Making a little more progress I get inside, find some shielded foes that are easy enough to dispatch, then a General comes in and I'm kind of reminded why I opt for a distanced strategy. I try to go in and hack away at limbs where I'm either swiped or hit with an AOE slam, then I make my retreat, heal up, and continue the repetition.
The concept of evaluating the encounter and picking out priority targets is pretty common, and I see that as just as much of an element of Doom's combat, if not moreso. Between enemy types present, level design, and weapons currently available to me my priorities might be completely different. In terms of weapon use, I don't see it as "USE BIG GUN", assuming you mean to just use what's strongest available at a given time. When I'm playing the shotgun/super shotgun is my bread and butter while everything else is situational. Even against hard hitters like the Mancubus, Arachnotron, Baron or Revenant, the super shotgun will usually be my go-to, but depending on enemy count, health, general ammo count, and level layout, I might go with the BFG, the plasma gun, rocket launcher, chaingun; I might even intentionally go for starting an in-fight between them. While the scope of an enemy's capabilities is far more simple in Doom, most enemies having a single means of attack, some also having a melee to use in close range, leaving only the Archvile to offer a secondary purpose, I think they intermingle to make for more interesting fights.
The thing I like about Doom's combat is just how calculated everything feels, projectiles are designed around dodging, you don't have specific regions to attack so you know in your head just how much ammo you need to spend to take down a given enemy, it's very crisp. By comparison, Shadow Warrior feels very messy, going back to the healing technique, a lot of the bigger encounters revolved around me shooting/slashing, getting hit, running away while using the healing technique, and going back to the fray -- I didn't feel this added an interesting back and forth or allowed me to be more aggressive, it just took away any real sense of high stakes knowing that I could always make my retreat and heal up again. And since healing had a cap at how high it would heal you, but not how often you could use it, it just resulted in a quicker loop of getting attacked, running away while healing, and trying to attack again.
I agree that the uzis actually do feel pretty good, but unlike Doom I don't have specific use cases for how I mix up what I use, outside of using the pistol or crossbow on winged enemies. In Shadow Warrior it often is just "USE BIG GUN" in the sense that I'm not really being explicitly aware of ammo use (and don't even know what my ammo count is until I switch to the weapon) and just use whatever's available to me. The uzis deplete quickly, so then I go to the next thing, then the next thing, then the next, there's no real sense of anything being more effective in situations over the other; some enemies will just as easily shrug off a four shell blast to the face as they will a rocket to the chest, and my ammo for everything just seems to disappear. I don't have any consideration for what I'm using other than what I have ammo for.
I just get way more satisfaction out of Doom as an FPS. Though from your response I probably didn't use the katana to its fullest, but speaking shot for shot I just think Doom is better executed.