They are both relative to the object thin and flat.
面 is connect with something vertical,realistic.一面镜子,一面墙,一面锣。
张 is connect with the thing horizontal.一张纸,一张相片,一张邮票。
In addition, 张 is connected with the action which needs to open, like 一张嘴,一张弓, 一张网。