Quite apart from the specific question but important to point out, the EA does not know what your max price range is.
He knows what your price range was for the other property. Why not express your interest in the cheaper property and play the game the other way. Compared to the house we wanted, it does not have x,y,z, so we would be willing to offer .... If only it had the ....
If a hotelier sees you coming out of a booked out 4-Star hotel next door and he is offering 3-star accommodation, do you think the hotelier would be expecting you to pay 4-star prices. Certainly your interest last time will affect how the EA approaches it, but with the right approach, you could meet him head on.
Consider going to see it with him, and rule it out. Wait a week or two, and make a reluctant offer.
Much of the above is of relevance assuming you are not referring to identical houses !