You aren't going to like the answer, but "it depends." Here's why...
Elevation is a Continuous Dataset. No matter where you plunk down a pointer, you'll be able to measure an elevation (in whichever format or reference you want to use). Continuous data lends itself really well to grid formats like DEM.
The biggest problem with continuous data is that it is technically infinite. We have to strike a balance between "accurate enough for our purposes" and "small enough to be feasibly workable." If we want to be "really accurate and precise," we could make the grid size infinitesimally small and we would approach a "real world" description of surface elevation... but at the same time the size of the dataset becomes impossibly large.
If you want to figure out a 'good' grid size, I recommend using a semi-variogram of your variable (i.e. "elevation") in your study location. It produces a graph of auto-correlation and distance~ at the sill distance, your variable is different enough to require another measurement: use the sill distance as your grid size.
A common enough practice -at least until LIDAR became more commonly available- was to take point location samples of elevation and then interpolate the surface elevations between them. Most of the old Topo maps were created in this way. And no few of the DEM files in use were created from the old Topo maps.
TIN surfaces are a method of creating continuous-like datasets using vector structures. The point elevation samples were not used to interpolate continuous data values at every location in between, but to "assume" that only the sample locations could possibly be considered valid data. ...So each facet of the TIN grows from its central sample point.
Both kinds of surfaces make "assumptions," but they each have their uses. TIN takes up a Lot Less Space on disk. DEM is usually data-heavy. The more sample locations used to build either type, the better the resulting model of real surface they describe.
Honestly, your question sounds like a good set-up for a research project.
