Both scopes would be good (ie...fun) for planets. They are both very small aperture for serious planetary observing. For back yard fun, just on any random night, both would be lots of fun and be fun to use in the 130x to 200x magnification range on average to better seeing conditions.
For Mercury, my money would be on the 80mm F/10 with FPL-53. More then likely you would be chasing the sun so it would generally be low in the sky. Atmospheric turbulence would probably equalize the size difference between the two, I'd give a slight edge to the 80mm F/10 with its superior glass. Basically you are trying to observe a star like object by observing Mercury. All you would really be doing was trying to get a tiny sphere out of Mercury and the 80mm F/10, like this one for example:
would probably punch a smaller hole near the Horizon and may acclimate faster to give you a cleaner shot of Mercury before it dips below the Horizon. It would be close compared to your AT-102ED but still, Id give the slight edge to the 80 F/10 with FPL-53 and Lanthanuma glass for its small hole needed and superior glass.
For Venus, again, I'd go with the 80 F/10, Venus is mostly about toning down its brightness. It also chases the sun so its usually never very high in the sky.
Venus is one of the toughest tests for chromatic aberration but eyepieces and its position in the sky are also a crucial part of getting a clean pristine view of Venus. I've seen some shading on Venus's body but it was using an AP 152 Triplet F12 Super Planetary refractor.
I think the 80 F/10 FPL-53 would deliver a slightly crisper view, easier to find that sweet spot for focus and may tone down any slight signs of Chromatic abberation on Venus. I had an AT-102ED, I dont remember any CA on Venus. So any advantage of the 80 or the 102 would be very slight.
For all the other planets, aperture should rule and the 102 F7 should provide more planetary surface details.
Should be able to pick up the polar caps on Mars easier with the 102ED, maybe some markings on the surface during the Mars close approaches and if seeing conditions are better then normal.
On Jupiter, the 102 F/7 should win because of more aperture. Its still just a 102, so even on ideal seeing condtions which are extremely rare, you may be able to see festoons on Jupiters body if you use a barlow and push the magnification in the 250x range, but again, that would a be very rare night. You should be able to see Moon transits across the surface with the 102ED also, but again, if would be a struggle to see a full lunar disk and its shadow traveling across the surface. Seeing black dots would be more feasible for its moons across the surface.Should be able to count the bands better with a 102 vs 80 mm if the seeing condition's were very good.
On Saturn, you would have a better chance of seeing more details on the Ring with the 102. Maybe seeing some ring divisions and surface shading details, maybe able to pick up more than just Cassini division with very clear seeing conditions.
On Uranus and Neptune, you need aperture and magnification. The 102 wins for Aperture and you'd have to barlow that scope and push the magnification to 200x plus to start making out and recognizing a blue disk on Uranus. Probably close to 300x to see a tiny dim blue disk on Neptune.
The Moon and Sun have their favorite scopes also, but they aren't planets.
you can see plenty of details on Jupiter for example, in General everyday use you'dd probably hit the atomospheric cei
Would there be any advantage of a 3" F10 refractor that has slightly better optics over 4" F7 refractor for planetary observing.
Note both of these are ED refractors.
The 3" has FPL 53 lanthium glass.
The 4" has just FK-61 glass.