Write a Python function `div_list(nums1, nums2)` that takes two lists of numbers, `nums1` and `nums2`, and returns a new list where each element is the result of dividing the corresponding elements of `nums1` by `nums2`. If the lists are of different lengths, raise a `ValueError`. If division by zero occurs, raise a `ZeroDivisionError`.
#### Example Usage
```python [main.nopy]
print(div_list([4, 5, 6], [1, 2, 3])) # Output: [4.0, 2.5, 2.0]
print(div_list([3, 2], [1, 4])) # Output: [3.0, 0.5]
print(div_list([90, 120], [50, 70])) # Output: [1.8, 1.7142857142857142]
```
#### Constraints
- Both input lists must be of the same length.
- Division by zero should be handled appropriately.