Yes. Not only are you reducing the image to 8-bit resolution, you are also applying compression algorithms which discard detail and can produce unwanted side-effects.
The best "processed" format you can choose is 16-bit TIFF, as this keeps bit resolution and does not use 'lossy' compression. PSD is an Adobe version of TIFF, which is well-supported but generally less compatible than TIFF.
If the image is always going to be processed by Photoshop, then PSD is probably the best format, as it offers proprietary advantages over TIFF.