Not aware of any NIB 81s as they haven't been imported in awhile now... You might find a safe queen/collectors sale, but certainly not in quantity. Most for sale now is Italian surplus that has come into the country the past few years. Some really fine/great condition examples among them though.
The 81s sights are pretty minimal/terrible. The 81 BBs are fairly improved, relatively. 83s you can replace both front and rear, while the 81s are just the rear since front sight is integral to frame. Nod to 83s for the win here.
B/c of all the safety mechanisms in 81 BBs, the 81s tend to have a better trigger however (firing pin block, trigger disconnector instead of block, etc.) And if memory serves, I think both 81s have a better trigger all things considered than the 83. Haven't shot my 83 in a couple years now.
The 81s barrels are removable, whereas the 83s are fixed. Nod to 83 on repeatable accuracy.
Re: recoil, I've only shot 81s in 32 acp and 83s in .380, so not 1:1. Slide weight on 81s is likely less however (haven't put on a scale though), so should be slightly less perceived recoil despite the alloy frame. 81BBs slides are very slightly beefier than 81s too.
Recoil on either of the 81s is mild -- I'd put it in the ballpark of +20-25% or so of shooting cci velocitor out a 22lr pistol.
The 81s tend to fill my hand more than the 83s especially around trigger finger, since 81s don't have scalloping on upper grips like like 83, so length of pull feels quite a bit longer. So, the 81s when decocked would be a challenge for most women to reach the trigger during the DA pull IMO. I bought my 81s primarily to be an option for recoil sensitive folks and a transition gun for new shooters, and it's really too thick of a grip for anyone with smaller than medium sized man hands... So I'm on the lookout for 82 Cheetah (single stack) or maybe another make/model instead for this role.
81s are definitely better looking.
81s takedown is more involved since separate barrel and needing to ensure recoil rod properly aligns with frame and takedown lever.
Haven't had any reliability issues w/ 81s, but then I don't shoot them terribly much due to not having .32 acp stacked deep pre-covid/subsequent price explosion like other calibers.
Wojtek makes new production firing pins for the 81s/all cheetahs, and that was historically the main weakpoint AFAIK when it came to long-term reliability.
So whether to buy really depends on your wants/needs/goals. Most folks will be more excited about a cheetah than a Cz83 however, but that's largely just on looks and brand name alone.