I just tried it, but the only problem is that I wasn't keeping my build order close to similar as I would've preferred. But the thing that it showed me is that both builds are very similar resource-wise; however, they differ in the point in which you get your first combat unit....
RAX -> SD
18 SCVs, 5 Marines, 1 MULE ... 25/27 Food ... 5:04/20:55
spending: eco-1700 , tech-550, Army-300 ... 2550
resources: 85m, 216g
First marine at 2:34
walled off at 3:42
SD -> RAX
21 SCVs, 4 Marines ... 27/27 Food ... 5:00/17:57
spending: eco-1850 , Tech-300, Army-250 .. 2400
resources: 230m, 496g
First marine at 3:12
walled off at 3:24
It wasn't perfect science due to me not adhering to a specific build very well, but the biggest thing that I'm looking at is the time in which you can get your first marine. Rax to SD has a 40 second advantage on SD to Rax and the wall-off times were somewhat arbitrary as I could've built it earlier, but I think I avoided it since I was building a Comsat anyway.
EDIT:
Although, I have no idea how quick a 6pool gets Zerglings to your base 😱.
First, note that this wasn't a 'perfect' run by any measure. I never build just marines so I winged it a bit, but I think it's an OK demo of the gist of things. So I get, at the 5 minute mark:
19 SCVs (20th is <1sec away), 1 MULE, 7 (8th is 2 seconds away, 9th is 9s away) marines, 29/43 supply (oops too many depots)
I have 2 rax up + 1 factory on the way. Adding a 3rd rax & always producing out of those buildings constantly, I have enough to expand by ~7min or so, along w/having a engineering bay down + combat shields going.
Spending: 1875/550/450
Resources: 100/128
1st marine at 3:15: could've been a bit earlier: 1) I started orbital command after rax1 finishes (drains all money); 2) in earlier parts, I go for constant SCV production over starting buildings earlier. I'd estimate that in sacrificing at most 1 SCV, I could probably get that first marine out by 2:50 or so. Or by trading off starting the 2nd rax later, I could finish the wall off by around 2:45.
last depot in wall started at ~3, done by 3:30.
Anyway, in fastest case, my first marine is no more than 30s slower than yours; and at worst, closer to 1min slower. But I can finish the wall off quite early. And my economic situation is quite a bit stronger.
Maybe I haven't been fighting the most competent/aggressive rushers, but I've never had a problem. And if/when you survive the rush, you're all set to counter-attack & expand, exploiting your advantage.