Assuming you're not doing some early cheese build, I'd think this would be something you could just do some math on to figure out which is better. Has this problem been solved? Which is better, and what is the math behind it?
Some smarter people than me decided to find an answer to this question. I'll quote the findings here
I used the AI to test the various builds in a very consistent manner, to try to answer the question once and for all.
The 9 overlord is the best economic build, period. Minerals at 2:15: 370
10 overlord can be used for 10pool and overpool, but is inferior to 9OL in every other possible respect to the tune of 10 minerals, and loses the small window of advantage it gets by building the 10th drone sooner by the time 10OL finishes its 11th worker. Minerals at 2:15: 355
A single extractor trick doing the trick before building the overlord (11 drones then overlord) gives a small time window of about a 15 mineral advantage, between workers 11 and 14, but there's a cost, of around 5-10 minerals. Best case, you might be able to break even when compared to 9OL, but most of the time you'll lose 5-10 minerals. Minerals at 2:15: 364
Single extractor trick after the overlord (10 drones, overlord, trick to 11 drones) is inferior to 10-T-OL in the 11-13 worker range, and is inferior to 9OL in the 14-15 range, so I honestly see no reason to ever trick this way, UNLESS you meant to 9OL, but forgot the overlord. In that case, this is your best way to try to catch back up, because the cost is 0-5 minerals instead of 5-10. Minerals at 2:15: 369
The double extractor trick provides such a small advantage over the single extractor trick during even a smaller window that it should probably only be used exactly to 12 pool, and even then, there is an extra cost over the single extractor trick. It probably compares to the single extractor trick much like 10OL compares to 9OL, meaning that if you're doing something exactly on drone 12, you might use it, otherwise, the single trick is probably strictly superior. Minerals at 2:15: 353 (imprecise, but again, likely strictly inferior to single trick except for fastest 12pool)
As if that was not enough here is a direct comparison between overlord on 9 and overlord on 10 (with extractor trick).
The image on the left is 9 and the right is 10+trick. Its also worth noting that the left player has 2 drones at that value, where as the right player has only 1.
tzenes' answer is here. His last part discusses this issue