They have the same precision but float has vastly larger dynamic range due to the 8-bit exponent. When normalized and quantized for output this does result in roughly the same effective dynamic range (depending on how much of the integer range was originally used).

The issue is audio is typically mixed close to maximum so any processing steps can easily lead to clipping. One solution is to use float or larger integers internally during each processing step and normalize/convert back to 24-bit integer to write to disk. Another (better imo) option would be to do all intermediate steps and disk saves in a floating point format and only normalize/quantize for output once.

I haven't worked with professional audio in over 25 years (before everything went fully digital) but I would be surprised if floating point formats were not an option for encoding and intermediate workflows. Many quantization steps seems like a bad idea.