In this case the cave is very small, only 50 meters, and there are only 14 survey stations. Retyping it into a Compass data file did not take long.
Compass and MeshLab do very different calculations to come up with volume. For my cave Compass gives about 2900 cubic feet and MeshLab gives over 20,000 cubic feet (about 585 cubic meters). Compass is doing a simple calculation based on polygons and using only centerline plus LRUD. MeshLab is a much more complex calculation based on a 3D model of triangles. Ultimately its calculation can be traces back to centerline, LRUD, walls, passage height objects and cross sections. Therion uses all of that to build a .lox file which, through translations, becomes the MeshLab file.
If it's that short, I would be tempted to do it manually, for a kind of sanity check. Pretend it's a cave made up from cuboids. Take the cross sectional area for each station (passage height * width), calculate the cuboid volume for each leg. See if it closer to one of the other. The MeshLab version seems like it might be doubling (or more) up, because of the way Therion generates cave tubes and passages from multiple overlapping 3D shapes, not a single "tube". One tube for the leg, then extra 3D shapes layered into the same 3D space for the wall drawings. If MeshLab is treating those as separate entities, rather than just the overall outer volume, then it will get a vastly larger measurement.