I think a significant difference between the Danish system and UBI is that working people do _not_ get Danish welfare. In the Netherlands we have a very similar system, except with a legal obligation to apply for jobs or do volunteer work in order to keep the welfare.
If I guessed correct, then the Danish is significantly different from UBI, because that system discourages working. Starting work means losing your welfare. Or at best every euro you earn from working is subtracted from your welfare. Besides that, in such systems you need a complicated bureaucracy to figure out who should and should not get welfare. This bureaucracy needs to contend with fraud, and is probably rewarded for giving as few people welfare as possible. This leads to a bureaucracy that is somewhat hostile to those it is meant to serve.
With Universal basic income, you lose the discouragement to work. You lose the very complicated and hostile bureaucracy (with exceptions for emigrants and immigrants probably). And you lose some of the political pressure to cut welfare, because everyone gets UBI so there is less jealousy.
In the Netherlands there have been cases of people on welfare needing to pay back thousands of euros because sometimes their mother did groceries for them. That was officially 'income' they failed to declare, and therefore their welfare was retroactively cut. That is just inhumane, and stupid. It means anyone on welfare who cannot make ends meet cannot ask anyone for financial help, because that would cost them their welfare.