Would either of our assertions be "right", or is it a matter of two people with incompatible worldviews?

Exactly. That's why we call matters like these a "moral dilemma", a case for either side could be made depending on the subjective views of the maker.

Eugh. Based off of what, exactly? Deontology might be haunted, but at least it's consistent.

Read more about WW2 history or refer to this History Stack-Exchange answer thread. The facts remain that:

1. Over half a million people were already killed in the "conventional bombing" that happened in the months before the atomic bombs were dropped in Hiroshima and Nagasaki.
2. The atomic bombs killed approximately 200,000 people.
3. Japan was not at all willing to surrender, it wanted to continue the war.
4. Dropping of the atomic bombs ensured that the war came to end, without which the "conventional warfare" would have continued until the Allies/Axis surrendered on their own and nobody knows when that could have been.

So logically, potential lives were definitely saved, at least that's what that thread seems to suggest but I'm open to different viewpoints on this though.

Edit

Regarding the "Civilian" argument, hindsight is twenty twenty. It has been a very recent and modernist approach to make a difference between "soldiers" and "civilians" and somehow concluding that killing the former is more morally justifiable than latter but this view hasn't stood the test of time yet. Also consider that during war times, the difference between civilian and soldier becomes hazy and WW2 was one of those extreme times.

The human ability to make systems, policies, and decisions based on something without any reference in the world outside of our imaginations isn't something to lauded.

Its incorrect to say that the decisions aren't based on anything outside of our imaginations, our rational thinking and moral capacity has been evolved through millennia of evolutionary experience after all, it doesn't sit in a vacuum? Every decision you take, the thought process you undergo for all kinds of things happens in the realm of a subconscious mind which is no less than a bio-computer awarded to the human gene by evolution.

"Right" or "wrong" are such easy concepts to use in an argument for why one should or shouldn't do something that almost every group or person that can be called "evil" has done it to justify their actions. Few people unironically see themselves as "evil".

I agree that many topics are complex and subjective, right and wrong are value judgments in many cases. There are even moral dilemmas where its not easy to decide whether doing a thing is right or not (for example, was it right/wrong to bomb Hiroshima and Nagasaki during WW2 even though it meant that the war ended prematurely and saving potentially lot more lives than it killed?).

But in cases like these (is it right/wrong to kill another sentient being?), I don't think there should be any moral dilemma in answering this question, every human with even basic moral capacity should be able to answer that question as non-affirmative.

Unlike other animals? I doubt it, there are many animals with great intelligence and cognitive-emotional capacity on planet Earth

There are but none have the ability to think, cognize and feel about things like pain and suffering in other beings. More importantly, none have the capacity to think rationally and the moral capacity required to decide that killing or harming another sentient being is a wrong thing.

They mostly act on instincts, compelled by hunger they kill other beings. But we do it only to satisfy our taste buds and despite having the moral capacity to know and understand that its a wrong thing, that's the utmost pity.

I'm quite new here. What is the "ratio'd" award?

That power doesn't imply a free will at all if you were already destined to change certain things in the universe at a certain time. What if the change didn't occur by your own spontaneous or deliberate "choice" but because of the complex web of cause-effect continuum in the cosmos just as it was meant to be?