I am comparing two different Digital Elevation Models
- SRTM (Datum: EGM96)
- Cartosat (Datum: WGS84)
How to convert WGS84 to EGM96 in ArcGIS Desktop?
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Vertical transformations are available for vector data at [ArcGIS Desktop] 10.5.1 and [ArcGIS] Pro 2.0. On-the-fly in Pro 2.1.
FAQ: Are vertical datum transformations supported in ArcGIS? suggests they may have been available in ArcGIS Desktop slightly earlier:
Vertical datum transformations are supported in ArcGIS version 10.4 and above. It is possible to apply a vertical datum transformation using the Project tool.
While it is possible to define the vertical coordinate system information for z-coordinates of several data formats in ArcGIS 10.3 and previous releases, vertical datum transformations are not supported in these releases.
For the latest ArcGIS Desktop help on this topic see Vertical datums.
Once we know the version of ArcGIS Desktop that you are using, and precisely what you have tried, we may be able to offer further assistance.
You cannot do a vertical datum transformation in ArcGIS. Give vDatum a try. https://vdatum.noaa.gov/