There are two completely separate questions here.
For the differences between DVD-R/RW and DVD+R/RW, I suggest reading the excellent article CDFreaks/MyCE member Spath wrote 14 years ago. None of the technical differences between + or - should make any difference to the longevity of discs. One could hypothesise that the superior tracking of DVD+R/RW might be advantageous when trying to read a badly degraded disc (and maybe that influenced M-Disc's choice), but I suspect with modern drives it would make little if any difference.
The significant differences between Verbatim Archival Grade and M-Disc DVDs have nothing to do with plusses or minuses, but is far more interesting.
The M-Disc DVDs are of a completely different construction to all other DVD±R (& CD-R) discs. Instead of an organic dye for the data layer and a separate metallic reflective layer, M-Disc discs use a single inorganic mineral layer. This has to be able to absorb enough energy from the laser during writing to undergo some sort of change so that data can be encoded onto it, but is also reflective enough not to need a separate reflective layer. Millenniata/M-Disc have always been very secretive about what this material is and how it behaves, and since the beginning most of their promotional material was very misleading (to the point of, it appears, occasionally being untruthful - for many years they claimed the data was "set in stone"). But it seems the material can best be described as a "glassy carbon".
Unlike M-Disc, Verbatim's Ultralife Archival Grade discs are not fundamentally different to convention DVD±R discs. They use a conventional AZO dye for the data layer and silver alloy for the reflective layer. What makes them different is that they have an additional gold layer, but this is not used as the reflective layer as was the case with early CD-R discs. Instead the gold layer is used as a chemically inert (and translucent) barrier to protect the silver layer from oxidation.