Comparing two different python counter objects

Those operations are already built-in to the Counter type:

Several mathematical operations are provided for combining Counter objects to produce multisets (counters that have counts greater than zero). Addition and subtraction combine counters by adding or subtracting the counts of corresponding elements. Intersection and union return the minimum and maximum of corresponding counts.

(Quoted from Python collections.Counter docs.)

So assuming D1 and D2 are Counters, try

R1 = D1 & D2
R2 = D2 - R1

If by shared letters you mean the Counter intersection, you can use the & operator and the amount of letters needed to convert R1 into R2 can be seen as the difference:

from collections import Counter

D1 = Counter({'A': 2, 'B': 1, 'C': 4, 'D': 5})
D2 = Counter({'A': 3, 'B': 4, 'C': 4, 'D': 7})

R1 = D1 & D2

print(R1)  # intersection:  min(c[x], d[x])
print(D2 - D1)  # subtract (keeping only positive counts)

Output

Counter({'D': 5, 'C': 4, 'A': 2, 'B': 1})
Counter({'B': 3, 'D': 2, 'A': 1})

If you want to keep negative counts, you can do it like this:

from collections import Counter

D1 = Counter({'A': 2, 'B': 1, 'C': 4, 'D': 5, 'E': 5})
D2 = Counter({'A': 3, 'B': 4, 'C': 4, 'D': 7, 'E': 3})

R2 = Counter({key: D2.get(key, 0) - value for key, value in D1.items()})
print(R2)

Output

Counter({'B': 3, 'D': 2, 'A': 1, 'C': 0, 'E': -2})

In the above example 'E' : -2 because the count of E is 5 in D1 and 3 in D2. Note: All the examples are in Python 3.5.