could be a small exhaust leak... sounds like it goes away after a while, that could because the exhaust pipe/flange whatever is leaking heats up and expands causing the gap to close some so its not as loud. Look, listen, and feel your way down the exhaust system from the manifold all the way back for where its louder, see if you can see any exhaust, and when i say feel, just run your hand along beside the pipe and feel for any exhaust puffing against your hand, not like grabbing the pipe, that could be bad.
Thats just one idea... i'm sure others will have some more idea's to what it oculd be, it could be just something as simple as yours being OBD-II and his is OBD-I... not sure if thats the case though.