NVIDIA showed some slides at MWC 2013 comparing Tegra 4 to quad-core S4 Pro (
http://forums.anandtech.com/showpost.php?p=34689618&postcount=230). Tegra 4 apparently is more than 2x faster than S4 Pro in SPECint2000, Sunspider, Web page load, WebGL Aquarium (50 fish), Quadrant Pro 2.0, Vellamo Metal, and is between 1.5-2x faster than S4 Pro in Geekbench, AndEBench Native, CFBench Native, Linpack MT (4T-Market), Antutu, DMIPS, Vellamo HTML5, while being only slightly faster than S4 Pro in Coremark. Strangely enough, NVIDIA somehow estimated the performance of Snapdragon 800 on a case by case basis. Now, take this with a huge grain of salt, but according to NVIDIA they expect Tegra 4 to have a significant performance advantage vs. S800 in SPECint2000, Sunspider, Web page load, WebGL Aquarium (50 fish), Quadrant Pro 2.0, Geekbench, CFBench Native, Linpack MT (4T-Market), Antutu, Vellamo HTML5, and Vellamo Metal, while Snapdragon 800 will have a slight performance advantage vs. Tegra 4 in AndEBench Native, and a significant performance advantage in Coremark and DMIPS. Tegra 4i is supposed to have 80% of the CPU performance of Tegra 4, but we will have to wait and see if that is truly the case across the board.