Bimanual input is frequently used on touch and tangible interaction on tabletop surfaces. Considering a composite task, such as moving a set of objects, attention, decision making and fine motor control have to be phased with the coordination of the two hands. However, attention demand is an important factor to design easy to learn and recall interaction techniques. This, determining what interaction modality demands less attention and which one performs better in these conditions is important to improve design. In this work, we present the first empirical results on this matter. We report that users are consistent in their assessments of the attention demand for both touch and tangible modalities, even under different hands synchronicity, and different population sizes and densities. Our findings indicate that the one hand condition and small populations demand less attention comparing to respectively, two hands conditions and bigger populations. Also, we show that tangible modality reduces significantly the attention when using two hands synchronous movements or when moving the sparse populations, decreases the movement time over touch modality, without compromising the traveled distance. We use our findings to outline a set of guidelines to assist touch and tangible design.