What kind of riding do you do? Frame size incorporates many different geometries that make up the center of gravity/moment of initia of the rider/bike. Changing the frame size will keep this roughly in the same place relative to each other to get the same feel from smaller to bigger riders in the same riding position.

Changing stem length will not have the same effect as going up a frame size as you are adjusting just one aspect of the frame geometry. It will merely shift your mass slightly forward which will shift the bike/rider COG forward traditionally putting more weight on the front tire and making climbing easier, while shortening the stem will have the opposite effect making getting behind the bike easier going down.

What I am getting at is increasing stem length will not have the same effect as increasing frame size as increasing frame size adjusts many geometries as opposed to one. It will merely bring you COG forward or backward which will change the feel of you body position over the frame.

Stems are fairly cheap so your best bet is to test it out but there may be other better choices to make your bike feel better for your riding style.