Width is the same, depth slightly different, profile looks to be the same.
Diameter is different. The 700C clincher is 622mm at the bead seat, the 28" tubular should be 632mm at the ID of the tyre. That usually means that the tubular rim's brake track will be at a slightly larger diameter than the clincher, but it depends on the height of the bead hook above the bead seat diameter. Sometimes you can get away with swapping from clinchers to tubs or vice versa without adjusting your brakes, but it's not guaranteed.
Diameter is different. The 700C clincher is 622mm at the bead seat, the 28" tubular should be 632mm at the ID of the tyre. That usually means that the tubular rim's brake track will be at a slightly larger diameter than the clincher, but it depends on the height of the bead hook above the bead seat diameter. Sometimes you can get away with swapping from clinchers to tubs or vice versa without adjusting your brakes, but it's not guaranteed.