I just call them whorlers so I don't have to type out "whorled phyllotaxy" every time.
As for your question, check out post #19 in my thread, including the quote of myself:
https://www.thcfarmer.com/community/threads/breeding-for-whorls.63887/#post-1264130
In short: because that 3rd leaf takes up an unoccupied spot it's an extra solar panel working for the plant and you basically get a lot more plant in the same time During vegging that is. Something that in practice - which is partly because I crop and spread them out - turned out the be the case as well as my IH#5 plant clearly showed (also in my thread). If you for example top plants to get a certain number of main colas you can top it sooner.
Once it matures and starts alternating there's no difference with a regular one, at least not that I noticed. I haven't grown and flowered and compared enough different ones yet to really make a comparison yield-wise etc but apart from getting extra bonus branches resulting in more bud sites I don't expect to find any major pros or cons either.
I got one flowering before it matured so the leaves in a main bud site is tri-whorled, so it has 3 axillary buds at the same level, but just a tad smaller than the 2 axillary buds at another similar but regular-opposite bud site so it sort of evens out.
I guess if there's a con it's that if it's a leafy indica with tight node spacing it indoors probably needs some pruning/training/trimming to prevent it from getting too bushy. Also depends if the side branches and the branches of those are tri-whorled as well.
