What would a world where we did the former but not the latter look like? It would be something like everyone having to be, at least in some measure, an entrepreneur--everyone would be their own small business, having to figure out what product or service to sell to others in order to make a living, and having to decide for themselves what use of their time would best serve that goal. That might well, in the long run (i.e., after all the upheaval caused by people who were used to having someone else define their business objectives, now having to do it themselves, has died down), be a big improvement over what we have now. But the key incentive of having to make a living is still there.
The "basic" part means that the level of income is generally set at an austere level. Think of living in the minimal existence of a monk. Some people would do fine with that, and would choose it, but the vast majority of people I believe would elect to work for more.
Humans over their history have always reached for more, including the most extremely wealthy, who basically have a capitalism granted equivalent of UBI, but significant numbers still choose to work.
And all history shows that that level increases over time to a point where "minimal existence" is enough luxury to be unsustainable. This is by no means the first time that the option of the state doling out basic necessities to everybody has been considered. The Romans had their bread and circuses. Today it would be food stamps and cable TV and Facebook and Twitter. Same difference.