Enneagram is an odd system in that it's less a logical all-encompassing map of personality and mainly nine archetypes of personality. One could say something similar about the 16 MBTi types, although there those types are being constructed of evaluation of smaller blocks (function pairs) which are then combined to create "types". However, enneagram assumes the archetypes themselves are the foundation and complete in themselves.
Wings and tritypes are basically ways (along with the variants) to expand on enneagram and provide additional flavor.
I'm not sure what the justification ever was regarding wings being confined to the two types to either side of an archetype -- aside from the word "wing" itself. The entire system seems more creative than rationally derived. In that sense, I don't really see wings as any better than tritypes. Wings work really well for some times, not as much for others. (Like, 5w4 is very common and seems to be reflected, for example, or 7w8, or 1w2 / 2w1; but maybe some of the other pairings, not so much or harder to see reflected IRL?)
Tritypes are just a flavoring that expands on enneagram archetypes by taking the prioritized type from each locus area (head, heart, gut), then looking at how the three enneagram types would likely play out in that personality mix with the archetypes prioritized a certain way. So at least it has the benefit of taking foundational pieces (the archetypes) and then logically building on how they would likely play out in proximity to each other. MBTI does this in but starts with the functional pairs as the building blocks, to build its own archetypes (the 16 types).
Anyway, as far as the most useful, since both wings and tritypes seem arbitrary? Probably tritypes, because at least it allows you to prioritize all the archetypes in a particular personality blend, versus wings, which just restricts you to influences on either side of an archetypes in the enneagram diagram which might or might not be categorically useful. But I consider the enneagram as just a way to describe a personality, rather than a system that covers the full delineated grid of personality (put another way, if you don't fall into one of the nine buckets, you land in dead space somewhere, rather than on a grid -- but the wings and tritype try to alleviate that a bit, which is why they spawned and evolved, to compensate).