Your question is Do you get a better BW if it's aged or does the quick/kettle method turn out something that is as good, or nearly as good?. That is probably a perspective call.
I pulled the following recipe from Brewing Classic Styles and have it going now. There were three options mentioned:
1 - Kettle sour add handful of grain to the kettle and maintain 100f for a day or two to get the desired sourness then boil as usual, killing the bacteria. The results may vary from batch to batch due to no control of the amount of bacteria in the grain.
2 Add a neutral ale yeast along with a Lactobacillus yeast to the primary and ferment as you would any ale (7 to 14 days until clear then package). The results should be consistent but may not get to an over the top sour.
3 Sour it with a Berliner Weisse blend for >6 months along with tasting and testing to get to the desired flavor then package.
All will probably work, but I am going with the second option for a quicker turnaround and more consistency than the kettle sour method. If it turns out I will be able to replicate it. The third option is probably more true to style and patience is a virtue but I have never been very virtuous.
Berliner Weisse (brewing classic styles)Brew Date
Grist
4.25lbPilsner1,871.1g
3.00lbWheat1,360.8g
7.125lbGrist total 3,231.8g
Hops
1.00ozHallertau4 %AA15
1ozHop Total
Yeast
1vialWhite Labs WLP011Pick one
1vialWyeast 1338
11gSafale 05
1vialWhite Labs WLP677Pick one
1vialWyeast 5335
Add neutral ale yeast along with Lactobacillus yeast in primary fermentation