We introduce a novel method based on physical proxies for investigating fundamental differences between touch and tangible interfaces. This method uses physical chips to emulate the flat, non-graspable objects that make up touch interfaces , in a way that supports direct comparison with tangible interfaces. We ran an experiment to test the effect of object thickness on participants' behavior, performance and subjective experience in spatial rearrangement tasks. We found that for the tasks tested, thick objects are faster but less accurate to operate, and that their graspability is only used occasionally. We also found that coarse manipulation of multiple thin objects is error-prone, an issue that only thick objects may allow to alleviate.