This is all generic information as texture cases can change from image to image, but it should apply to the majority of examples you would come across.
If doing a 1:1 conversion of the same format, BC7 to BC7, DXT5 to DXT5, etc., the pixels in the result will not change... much. This depends on which program you use. TexConv and Compressonator usually won't be much different, ImageMagick on the other hand is not as sophisticated when it comes to DDS textures, so using it you will lose far more quality than the other programs.
If doing a 1:1 conversion of different formats, BC7 to DXT5, DXT5 to BC7, etc... The pixels in the result will change a bit more. There will be noticeable loss no matter which format is chosen as the input or the output. The more conversions done, the further the result will be degraded. Lossy to lossy always results in more loss. I imagine it would eventually bottom out, where "perceived quality" does not change. I honestly don't know, I haven't tested this much. The only time I see doing a 1:1 conversion would be BC7 to DXTn for compatibility with older hardware.
If rescaling, BC7 will always have higher quality than DXTn formats regardless of the input format. I believe the entire image is recalculated before it is compressed. In this case, rescaling DXTn to BC7, will have higher quality than DXTn to DXTn. Usually a bilinear filter is applied when scaling up or down by default using just about any program. Some programs allow adjusting the filter used, although I do not allow that in my script as to not further complicate things. For downscaling, this is fine, for upscaling, xbrz and waifu2x do a better job than any of the DDS programs.
To sum it up, if all that is available is a DDS pack, there is no point in doing a 1:1 conversion to any other DDS types. If downscaling a DDS pack, always choose BC7 for higher quality, even if the pack was using DXTn. If upscaling, xbrz or waifu2x to PNG then convert to DDS (BC7).
If doing a 1:1 conversion of the same format, BC7 to BC7, DXT5 to DXT5, etc., the pixels in the result will not change... much. This depends on which program you use. TexConv and Compressonator usually won't be much different, ImageMagick on the other hand is not as sophisticated when it comes to DDS textures, so using it you will lose far more quality than the other programs.
If doing a 1:1 conversion of different formats, BC7 to DXT5, DXT5 to BC7, etc... The pixels in the result will change a bit more. There will be noticeable loss no matter which format is chosen as the input or the output. The more conversions done, the further the result will be degraded. Lossy to lossy always results in more loss. I imagine it would eventually bottom out, where "perceived quality" does not change. I honestly don't know, I haven't tested this much. The only time I see doing a 1:1 conversion would be BC7 to DXTn for compatibility with older hardware.
If rescaling, BC7 will always have higher quality than DXTn formats regardless of the input format. I believe the entire image is recalculated before it is compressed. In this case, rescaling DXTn to BC7, will have higher quality than DXTn to DXTn. Usually a bilinear filter is applied when scaling up or down by default using just about any program. Some programs allow adjusting the filter used, although I do not allow that in my script as to not further complicate things. For downscaling, this is fine, for upscaling, xbrz and waifu2x do a better job than any of the DDS programs.
To sum it up, if all that is available is a DDS pack, there is no point in doing a 1:1 conversion to any other DDS types. If downscaling a DDS pack, always choose BC7 for higher quality, even if the pack was using DXTn. If upscaling, xbrz or waifu2x to PNG then convert to DDS (BC7).
