GMTED is definitely the most inaccurate provider, but it has world wide coverage. So the Multi provider uses either CGIAR or SRTMGL1 inside of the SRTM bounds and outside it uses GMTED.
CGIAR and SRTMGL1 are both based on the SRTM data. This data contains voids and incorrect measurements. Some good information can be found here.
CGIAR is based on the SRTM 3° data, which is not as accurate as SRTMGL1, but CGIAR used algorithms to improve the data, but the data is not as precise as the SRTMGL1 (1°). Both CGIAR and SRTMGL1 are void filled.
CGIAR is IIRC about 90*90m in resolution. SRTMGL1 is IIRC about 30*30m in resolution.
But it’s not that easy. SRTMGL1 still contains incorrect measurements. CGIAR has been improved with algorithms to fix incorrect measurements. So I think it’s valid to say that SRTMGL1 is more precise, but CGIAR contains less errors.
You should definitely use GMTED outside of the SRTM area. The question is if you should use SRTMGL1 or CGIAR inside of it. Since you reported better results with SRTMGL1, this might be the way to go.
Some more information on this can be found here as well: