So they are already at preschool but you are wondering about nursery? Nurseries that run from 0-5 are usually open working hours to provide childcare for working parents. Pre-schools usually are just open school days and term time . If you are using it for childcare pre-school is less flexible. If the pre-school is attached to a local school they are more likely to meet children who will start reception with them. Educationally they should offer the same as they follow the Early Years Curriculum.
You can't judge on what it's called, as the words are interchangeable.
If it's a school (maintained) Nursery with a teacher in charge, then they will have a higher ratio (1 adult to 13 dc) whereas in a setting that doesn't have a teacher in charge, the ratio will be 1 adult to 8 dc.
You need to think about the times they start / finish and the logistics of that.
You need to find out how the new Nursery works in terms of how they offer the 15 hours (might be over 2.5 days for example - does that fit with your other commitments.
Some places called 'nursery' are actually the same as what others call 'pre-school'
All should be following the same curriculum (EYFS).