Good replies here already but I'll chime in.
We have two very different microbes for souring: Lactobacillus spp. (Lacto) and Pediococcus spp. (Pedio). Both may be referred to as LAB (Lactic Acid Bacteria).
Lacto works very quickly to make a clean sour. Does not tolerate hops well during souring but you can sterilize and add hops after souring if desired. Either wild bacteria (e.g. sour mash) or lab cultures can be used. Using a sour mash technique and/or wild bacteria may produce added flavors (some of which may not be desirable). Any yeast can be used post-souring.
-Fast turn-around (a couple days beyond any regular "clean" beer)
-Predictable result from lab cultures
-No risk to equipment if sterilized
-No "funk" ... Unless you want to add Brett of course and give additional time. No one is stopping you.
Pedio takes much longer and must be used in combination with Brettanomyces spp. (Brett). Pedio is hop-tolerant. Brett takes a long time, dries out the beer, and add any number of a large potential variety of flavors a.k.a. "funk". Potential to be much more sour. Wild microbes, dregs, lab cultures, anything is fair game. Plenty of time to impart oak if desired.
-Produces more interesting beer that is unparalleled in potential flavor complexity
-Less predictable, depending on technique and source of microbes.
-Takes longer to ferment (6-24 months)
-Potential for contaminating clean beers used with the same cold-side equipment.
As far as technique...
Neither of these approaches are necessarily easier than the other.
Brett is slow to start, so whether you pitch it with Sacc or later, it won't make a huge difference in the long run.
Pitching Pedio earlier rather than later might be beneficial for making it more sour.
Depending on the species, strain, temperature, and amount of hops, giving Lacto a head start in a mixed fermentation should generally produce a more sour beer.
It's worth mentioning that we also have the option to do a 100% Brett fermentation on a Lacto kettle sour. This should be a relatively fast turn around sour (Brett doesn't fully attenuate when used alone) with a limited amount of Brett flavor from whatever species/strain was used (YMMV), similar to different Saccharomyces cerevisiae strains.
If you just love funk you CAN also use Brett for less sour or non-sour beers, something like an oud bruin for example or a pumpkin ale.
I can think of some other experimental techniques that might produce interesting results as well... Definitely have some room for experimentation.
Hope this helps clear things up. Cheers!