It seems to me there is a lot of confusion about how gear ratios work in this thread. Let me comment on a few and offer my view on why SRAM cassettes are just a bad design and some Shimano cassettes are terrible as well along with one objective way to measure it.
You don’t understand gear-distance. If you reduce chainring sizes the absolute “gear-inches” jumps get smaller even though the ratio differences remain the same. Everything you think the 13t jump up front is responsible for is actually enabled by the 10t cog.
Gear inches is an irrelevant concept for the discussion as we keep wheel diamater the same. What is left is only ratio of number of cogs in front to numbers of cogs in the back.
Yes the absolute jumps in % terms between cogs on the AXS cassette are slightly larger, but they do not feel as large due to the smaller chainrings. Imagine the chainring size acting like a 'scaling factor' to the cassette. The bigger the chainring the higher the jumps will be in real life. Even if the same cassette is used jumps will feel smaller with a 50t than a 53th chainring and smaller still with a 34t chainring.
I am not going to offer any maths here, you can use gear inches calculator to work out numbers.
Again, using gear inches in this discussion is a sign of confusion. It doesn't matter how big rings are in front, only gear ratio matters.
As an example: if you have 32 in front and 11-32 cassete and compare it to 34 in front and 11-34 casette the only reason the last jump feels bigger in 32 system is because 32/28 is a bigger number than 34/30. 32/28 is 14.3% jump while 34/30 is a 13.3% jump. It has absolutely nothing to do with the front ring being bigger.
If you want a 1:1 low gear and a 4.6:1 high gear, for example, these are your options:
Shimano 50/34 with 11-34
Sram 46/33 with 10-33
These are the jumps on the cassette:
Shimano 9.1%, 8.3%, 7.7%, 7.1%, 13.3%, 11.8%, 10.5%, 14.3%, 12.5%, 11.1%, 13.3% (ave. 10.8%)
Sram 10.0%, 9.1%, 8.3%, 7.7%, 7.1%, 13.3%, 11.8%, 10.5%, 14.3%, 16.7%, 17.9% (ave. 11.5%)
Yes, although average jump is not the best metric as it will always be the same in the cassete of the same range. You need to measure standard deviation of jumps to see which cassette has more equal jumps. I've written small script for that. Here is the output for some popular cassettes:
11 speed ultegra 11-30:
11 speed cassette
['11 ', '12 ', '13 ', '14 ', '15 ', '17 ', '19 ', '21 ', '24 ', '27 ', '30 ']
['1.091', '1.083', '1.077', '1.071', '1.133', '1.118', '1.105', '1.143', '1.125', '1.111']
average jump: 1.106
Std dev: 0.023
11 speed ultegra 11-32:
11 speed cassette
['11 ', '12 ', '13 ', '14 ', '16 ', '18 ', '20 ', '22 ', '25 ', '28 ', '32 ']
['1.091', '1.083', '1.077', '1.143', '1.125', '1.111', '1.100', '1.136', '1.120', '1.143']
average jump: 1.113
Std dev: 0.023
11 speed ultegra 11-34:
11 speed cassette
['11 ', '13 ', '15 ', '17 ', '19 ', '21 ', '23 ', '25 ', '27 ', '30 ', '34 ']
['1.182', '1.154', '1.133', '1.118', '1.105', '1.095', '1.087', '1.080', '1.111', '1.133']
average jump: 1.120
Std dev: 0.030
10-33 SRAM:
12 speed cassette
['10 ', '11 ', '12 ', '13 ', '14 ', '15 ', '17 ', '19 ', '21 ', '24 ', '28 ', '33 ']
['1.100', '1.091', '1.083', '1.077', '1.071', '1.133', '1.118', '1.105', '1.143', '1.167', '1.179']
average jump: 1.115
Std dev: 0.034
10-36 SRAM:
12 speed cassette
['10 ', '11 ', '12 ', '13 ', '15 ', '17 ', '19 ', '21 ', '24 ', '28 ', '32 ', '36 ']
['1.100', '1.091', '1.083', '1.154', '1.133', '1.118', '1.105', '1.143', '1.167', '1.143', '1.125']
average jump: 1.124
Std dev: 0.026
11-34 ultegra cassette has a huge jump between 11 and 13 (18.2%!) I am not sure what the justification for that design was. Probably it was just more convenient to manufacture for whatever reason. Here is a sample cassette that improves over it:
[11,12,13,15,17,19,21,24,27,30,34]
and the output of my script for it:
11 speed cassette
['11 ', '12 ', '13 ', '15 ', '17 ', '19 ', '21 ', '24 ', '27 ', '30 ', '34 ']
['1.091', '1.083', '1.154', '1.133', '1.118', '1.105', '1.143', '1.125', '1.111', '1.133']
average jump: 1.120
Std dev: 0.021
As you can see average jump is the same as with the old one (it always is) but standard deviation is lower meaning less variance in jump sizes. It's worth noticing Shimano rectified that mistake with 12 speed which is exactly the same as my improved 11 speed cassette starting from 15 cog. Whatever "reason" there was for a bone headed design in original 11-34 no longer applies apparently.
As to SRAM cassettes let's take 10-33 for example. It could be improved like this:
[10,11,12,13,15,17,19,21,24,27,30,33]
['10 ', '11 ', '12 ', '13 ', '15 ', '17 ', '19 ', '21 ', '24 ', '27 ', '30 ', '33 ']
['1.100', '1.091', '1.083', '1.154', '1.133', '1.118', '1.105', '1.143', '1.125', '1.111', '1.100']
average jump: 1.115
Std dev: 0.021
Or if you positively hate the idea of jumps in the back getting smaller relatively speaking then like this:
[10,11,12,13,15,17,19,21,23,26,29,33]
12 speed cassette
['10 ', '11 ', '12 ', '13 ', '15 ', '17 ', '19 ', '21 ', '23 ', '26 ', '29 ', '33 ']
['1.100', '1.091', '1.083', '1.154', '1.133', '1.118', '1.105', '1.095', '1.130', '1.115', '1.138']
average jump: 1.115
Std dev: 0.021
Both designs have much lower standard deviation between jumps than the original one and thus would feel much smoother - you would need narrower cadence range to ride it.
SRAM designed their cassettes with mountain biker philosophy of going up the hill whatever way, preferably chilling and talking to your buddies and then having fun bombing it downhill. The problem is that in road cycling you spend 3x or 4x as much time climbing and that's where the biggest time differences arise - where the races are won and lost. If you want to spin comfortably up the hill you need closer jumps at the back. It's not like the hill is going to be 7% all the way up. It's going to be sometimes 5%, sometimes 8.5%, sometimes 11% and sometimes 15%+. I doubt SRAM designers ever rode in the mountains without taking a bus to the top.