Both the HTC One and Galaxy S4 use Qualcomm's Snapdragon 600 system-on-a-chip (SoC). But the processors are a bit different: The HTC One comes with a 1.7GHz quad-core Krait 300 processor, while the North American version of the Galaxy S4 comes with a slightly faster 1.9GHz Krait 300. So Samsung's device gets a bit of an edge here. For the record, Samsung also released an international version of the new phone with an eight-core Exynos 5 Octa SoC.
Both devices come with 2 GB of LPDDR3 RAM, and both devices also user Qualcomm Snapdragon's Adreno 320 GPU for graphics power, so the two smartphones are evenly matched in the memory and graphics departments.