If I understand it correctly, the key difference is that it is now up to the individual schools.
One school may have translated the new curriculum content into a 'levelling' system that is just as detailed as the old levels were, with very clear, detailed criteria of what a child must achieve in order to reach which level. Another school may choose to restrict 'levelling' to vague, generalised 'child is on track/not on track' information, based solely on the teacher's 'impression'. (The latter school may have more time to actually teach, but at the cost of having less precise 'data' of where each individual child is at and how much progress they are making)
Even if your school has implemented a system that you find helpful, they may still have the problem that they can't compare their internal 'levelling' with other schools. What's the term - when teachers from different schools came together and compared how they levelled they same piece of work, to ensure that everyone's levelling was realistic (not too strict/too optimistic) and comparable.
And you may have the problem that whereas with the old levels, you could look up the detailed criteria online (or ask Mumsnet to 'level this piece of work for me please'), now only teachers from your school can tell you what 'level' your child is working at because those particular levels may only exist at your child's school.
Our school seems to have come up with a decent system, and clearly they have put a lot of thought into it, which makes me feel optimistic. We will be told in which year's curriculum our children are working (that would be the old 'level' except that they go from 1-6 now rather than 1-4), and how secure they are in it, with 6 'sublevels'. Furthermore we will be told how that translates in terms of expected attainment at end of their Key Stage. So e.g. if a year 3 child is working at year 3 curriculum at 'secure' level, right at the start of year 3, that would translate into 'expected to achieve higher than 100' at the end of KS2, provided the child continues to make the expected progress. If at the end of year 3 the child is still 'secure' at the year 3 curriculum, that would translate into 'expected to achieve about 100' at the end of KS2 and would indicate that the child has made less progress than expected in Y3.