The reason they look a bit off is because Q2W uses deluxe mapping, which is alot more inaccurate and tacky than Xreals relief mapping. If I were to use those in xreal ( and I have ) with the heightmap, they look much tider.
Deluxemapping and reliefmapping are not equivalents which can be compared

Anyway, I think I know what you mean. Let me see if I can put it right:
- Bumpmapping is a per-pixel technique to generate shadows to each pixel
- Reliefmapping is a per-pixel technique to generate volume (height, as in a terrain) to each pixel.
- Specular mapping is a per-pixel technique to generate light reflections to each pixel.
- Deluxemapping is a lightmap technique to store face-relative surface direction to each pixel which can be used to generate the bumpmapping shadows or the specular mapping reflections.
This means. XReal has bumpmapping which is generated to each pixel in real time, allowing the lights to dynamically change. It also allows to generate specular reflections from several light sources. It also has reliefmapping.
Quake2World has bumpmapping which is generated to each pixel from a precomputed deluxemap (a lightmap of directions). Not allowing lights to dynamically change nor being able to overlap several specular mapping sources. It also has reliefmapping? (I don't know if it does or not, but I guess so).
BTW, Deluxemapping is what Warsow uses too. Nexuiz uses it as default also, but optionally does both. XReal used to have optional deluxemapping too, dunno if it's still there.
The second method is much faster to render. The first is more complete.