They appear to be totally different optical formulas.
- The SP AF 28-75mm f/2.8 XR Di LD has 16 elements in 14 groups
- The 28-75mm f/2.8 Di III RXD has 15 elements in 12 groups
Although they are both the same diameter and use the same filter size, the newer shorter registration lens is 25.9mm longer. The difference in the registration distance between the E-mount and the A-mount is 26.5mm.
In terms of maximum magnification and minimum focus distance:
- The SP AF 28-75mm f/2.8 XR Di LD has an MM of 0.2X at an MFD of 33cm
- The 28-75mm f/2.8 Di III RXD has an MM of 0.34X at an MFD of 19cm at the wide angle end of the zoom range. Typically MM for most zoom lenses come at the longest focal length, where this lens has an MM of 0.25X at an MFD of 39 cm.
The older lens was introduced way back in 2008, the newer lens came out a decade later in 2018. During that decade, Tamron has upped their game considerably in terms of optical performance, and the prices of the newer lenses reflect that. Tamron themselves describe the older lens as a "mid-range zoom", and it's not altogether clear they're referring only to the focal length range, since there's no mention of "mid-range" in the newer lens' description at their USA website.
Because the two lenses are ten years apart in terms of design and introduction, it's difficult to find a good side-by-side comparison shot under the same conditions using the same camera.
This comparison at The-Digital-Picture used a 21MP EOS 1Ds Mark III (of 2007 vintage) for the older lens and a 42MP Sony α7R III (from 2017) for the newer lens. But even a cursory look at the test images from each should be enough to see these two lenses are in entirely different leagues.