I get the feeling that maybe there's a little miscomunication between you and the builder. Since you say he's offering you a choice between alum. drip edge and gutters, he may be talking about the devices that spread the water when it comes off the roof, which are touted as being better than gutters because they don't clog up with leaves. Another reason for my thinking is that drip edging is not normally alum., it's galvanized tin. Another, as has been pointed out, is that codes require drip edge to be installed. I can't imagine a builder offering me a choice between drip edging and gutters. I would question his competency. I'd ask him to show me what he's talking about. That will probably clear it up. As for inspections as suggested by bc the cost would vary depending on your area, how much the inspector is asked to do and how many times you want it inspected.