The second stage is about twice the size of the New Shepard, which costs around 10 million to produce. So assuming their second stage cost is ~20 million, that would be around double of the Falcon 9 second stage cost, e.g. they are at a disadvantage of 10 million there. They can easily cover that by offering dual launches and having a cheap reusable first stage.
BO is really different from SpaceX in the sense that Bezos isnt involved much, he is only the money. The people that create the strategy at BO are people who are industry veterans while at the same time not satisfied with how the industry works. A lot of people who worked at the actually first rocket than landed vertically (Delta Clipper) ended up at Blue. So the strategy at Blue is to drop one rocket that can capture the whole market, so the number of launches will be maximized, which will lower the cost even more.