W.P.
Dear L.:
Here is an ugly truth (with very few exceptions): Your biological child and your step-child will not be in the same position. If you divorce (or break-up if not married), your child will stay with you and your step-child will go away, whatever 'with you' and 'go away' means in detail.
I tried to explain that to my now ex-wife BEFORE we got married, and for seven years it went well. But when she slept around and we had to split, there it was again. At least you are both in the situation of one own and one step child.
Perhaps you should agree on the most important disciplinary measures: The A list of things earns a spanking, the B list a time-out, the C list a verbal admonishment, etc.
If you are incompatible, you may have to reconsider your future together. If his alternate ways of discipline work, you may even do things differently, as long as you agree on what is acceptable and what is not.
My 2 cents,
W.