Ovinomancer
No flips for you!
It took me a bit to figure out what you did to get it, but I did recreate your numbers. First, let me explain what I understand you did so we're on the same page.
The above charts look only at the chance that the PC kills the target in that round. For the single big attack, it's straighforward enough. You kill it or you don't. The cases are round 1 hit, round 1 miss round 2 hit, round 1&2 miss round 3 hit, and so on.
The second case has more cases to consider, and these expand rapidly per round. You still kept the analysis at the single point where PC 2 kills the creature in that round. So, on round 2, you consider the case for round 1 - 2 misses and round 2 - 2 hits, round 1 - 1 hit and round 2 - 1 hit and 1 hit round 2, and, finally, round 1 - 1 hit and round 2 - 2 hits. And so on.
However, in both cases, I think you've made an error in analysis. Each round should have the cumulative chance that the creature is killed in that round or in any previous round, not just the chance that the target is killed in that round. You're essentially ignoring all the cases where the killing is done already. But, let me drop some illustrations first.
Here is 3 rounds of expanded hit cases and associated odds for each for PC 1:
And here is the same for PC 2:
You can see that the column marked % Kill the round shows the numbers you presented. The column marked % Kill Overall is the total odds at the end of each round that the PC is standing over a dead body. As you can see, PC 1 is ahead in rounds 1 and 2, but starts to lag behind in round 3. This continues, although it remains close, because the number of successful kill cases for the 2 attack character grows faster. This is why there is a larger delta in round 1, where PC 2 has 1 kill case out of 4 and PC 1 has 1 kill case out of 2, and almost none in 3 and four due to the similarity in kill cases. Past 3 rounds, the % Kill Overall is essentially 1 for both characters.
So, overall, your average rounds to first kill seems a bit wonky, as it's ignoring the odds of a previous round resulting in a kill already. I'm not sure that your number tells us anything, and, honestly, I'm not sure you can just add up your percentages to get to an average time to first kill. The extended results above, though, do suggest that the single big hitter will kill first, and possible more often. I crunched some more numbers to look at this in a case where there's always at least one more foe to attack. So, over 3 rounds:
PC 1 kills none 6% of the time, 1 29% of the time, 2 43% of the time, and 3 22% of the time. This is an 'at least 1' of 94% and an at least 2 of 65%.
PC 2 kills none 4% of the time, 1 41% of the time, 2 50% of the time, and 3 5% of the time. This is an 'at least 1' of 96% and an at least 2 of 55%
It's very interesting, I'd say. The single big attack spends more time at the ends than the multiple attacks and less time in the middle. What's also interesting is that the average damage output per round for both PCs remains constant and equal -- as you might expect. This was one of my primary checks for my maths - did I maintain expected average damage per round?
And, all of this is using your numbers. Some have advanced this use case is maximized for the big hitter based on target hp, but the analysis is stable for all x less than 9 and greater than 4. Until you get into the hp that PC 1 can't kill with 1 hit or into hp that PC 2 can kill with one hit, the numbers don't change. However, if you use different numbers, the analysis will change. This assumes that big hit precises doubles little hit, and that's not a valid assumption, nor is it valid that big hit will always kill and little will not. Different cases may yield very different outcomes. It should be possible to build an expanded case chart that could handle very different numbers, but it would take more work than I've done so far (a good bit) so unless there's a lot of interest, I'm not going to try.
