I would have to say I think how we approach a project is pretty much the same, but that our finished products are different. I don't know that there is any way to quantify "how," since every site and every client is different. Hell, I probably would design some of my old courses differently if I had them to do over again, so you can't even compare me to me!
At Sand Hills and at Kapalua, I walked away thinking (maybe "hoping" would be more accurate) that I would have made the same decisions that Bill and Ben made. Since then, while there's not a single one of their courses I haven't admired, there's also not one where I thought I would have done the same thing they had done. This includes Friar's Head ... certainly we could have built something there, but I don't think we'd have done the same thing.
And I'm glad we are not building the same things ... or both copying Seth Raynor's style. Vive la difference!
I think in the most general sense, our styles are similar because as Tom Paul pointed out, we are less likely than practically any other architects today to move earth in the fairways. But certainly we've both done courses where we had to, and did, and as I get better at it I'm not afraid to do things when the mood strikes. Pacific Dunes has 3-4 places like that which no one seems to have noticed.
I think Bill's green designs are a little more restrained than my own. I remember taking him around Lost Dunes during construction and his eyes were wide ... that was after we'd walked Notre Dame in the morning and I'd been impressed by how subdued it was. But, in Oregon and in New Zealand, I've been more restrained.
Certainly we are both also big believers in surrounding ourselves with talented people and letting them help ... we both learned that from Pete Dye. So it's never been just me vs. Bill. In New Zealand right now it's me and Bruce and Eric and both Brians and Chris Hunt and Dan Proctor, and I will say that Bill and Ben themselves couldn't touch that team ... but they wouldn't try to go it alone, either.
I hope they do take the job to do the third course in Bandon, because I'd love to see what they can do there ... although, if the roles were reversed, I'm not sure I would want to take the inland property and compare the result to Bandon and Pacific Dunes. In any case, it looks as though we will be designing courses side by side on a project a couple of years out [sorry, I can't divulge any specifics at this time], and we are all looking forward to looking over each other's shoulders while we work.