Most of the Basic Income proposals I've heard don't go as far as covering basic needs very well; meanwhile there will be money available working to provide for people who aren't able to get enough of their needs currently met. And if you want nice things, you'll still have to work.
There aren't zero parallels to the USSR, but it's really not going as far, and I expect the human responses to be different.
Neither the basic needs were covered very well in the USSR, at least as I've been growing up in 80s. E.g. jeans already had been a luxury item. Housing, medicine etc. available for the most people were way below "poor" of the western world. I grew up in a 12 m^2 room in a 3-room flat shared with another family and was lucky, because many of my parents colleagues lived in dorms.
I am aware that the BI proponents believe that jealousy is a stronger drive than apathy. And this is undoubtedly true for some fraction of humanity. I just think they overestimate how big is this fraction.
Not jealousy per-se, but the drive to want more. People work long after basic needs are met.
I admit my understanding is somewhat shallow, but I think the problem with the USSR had at least as much to do with price controls as any cash transfers. In a capitalist system with BI, if there's a labor shortage the wages paid to labor will increase and the price of goods will increase accordingly, and people will be motivated to take those jobs as the BI payments shrink in purchasing power. The HUGE advantage is that when there is a labor surplus, those people that remove themselves from the work force (voluntarily, involuntarily, or semi-voluntarily) still play a role in aggregate demand.
It does not matter what you call it but people who had their basic needs covered for generations do not just go and work because they want more. Some do, most - don't. Even as the USSR had been crumbling down and the cheap government goods had became hard to find people would rather go and line up for many hours to buy everyday groceries than do something to earn more money and buy much better goods without much hassle.
This phenomenon is not very noticeable on small scale (both in population and time). So I'd recommend paying a closer attention to the USSR history and being a bit critical to the "we overspent them" or "they did not do socialism right, duh" explanations. In my opinion, if it's been possible to overspend a superpower that had its own spaceships then overspending small fry like Libya, North Korea or Iran would not take any time at all. And free market just does not work when people have their basic needs covered.
There also had been very small free market in the USSR and it was so small not because communists had been screwing with it (at least not more than the western governments screw with their markets), it's been small because most people just ignored it. If they could not find something in the government store then they would not buy it, even if they could afford the free market price.
While I'll certainly give it some more thought, and grill my acquaintances who have more than a passing familiarity with the subject (both natives and academics), I am still not sure it's a very good model for the generic circumstance of handing out some chunk of value for people to build on; there are way too many confounding factors.
Those in the USSR didn't suffer only the meeting of their needs, but also a constraining of their hopes; the cultural mythology glorified the state, not individual achievement; quotas frequently lead to poor results; and, quite importantly, I would expect that outright oppression contributes something to the breaking of a people - I believe there were several examples of groups taking initiative to better their lot and winding up dead, which seems strong incentive not to try.
What actually contributed to the "fall" of the USSR is a somewhat orthogonal question. A decline in worker efforts certainly might have contributed. I've been under the impression that a significant problem was the politicization of scientific and economic questions, in ways that just didn't square well with reality - I know that in particular they were slow to take up computers, and an ideological commitment to Lamarckian evolution lead to poor agricultural planning.
There aren't zero parallels to the USSR, but it's really not going as far, and I expect the human responses to be different.