The 55/2.8 uses floating optics, the 55/3.5 has fixed elements and is optimized for 1:10 images. It's still a sharp lens. I end up using the 55/2.8 more than the 55/3.5.
I have a 55/3.5 and a 60/2.8 AF-D. When I made extensive comparisons to decide which lens I would use for repro, I found that the the 55/3.5 was noticeably sharper at 1:10, and that the 60/2.8 was noticeably sharper at 1:1, so I kept both and use one or the other depending on the ratio.
When I'm duplicating slides, I'm shooting at pretty close to a 1:1 ratio. I didn't realize the 55/3.5 was optimized for such a non-macro magnification. But perhaps this explains why my 55/2.8 AIs is noticeably sharper at my dupe magnification than the 55/3.5. Interesting.
I'm going to add an "oddball" recommendation -- a Tokina 24-40mm f/2.8. This stubby lens served me will until I swapped it out for an autofocus wide angle zoom. As usual with Tokina lenses from this era, it's very solidly built, has a next-to-useless lens hood, and by modern standards flares too easily.