Yes, the Core i3 can limit overall game performance. But games should still play better on the laptop with the Intel HD 4000 because it is more powerful than the Intel HD 3000.
I tested the Intel HD 3000 in my Lenovo IdeaPad Y470 in a few games (I disabled the nVidia GT 550m). I used it to play Fallout 3, Skyrim, and Mass Effect 3. The games were playable to a certain extent. Performance was mostly below 30 FPS with extensive editing of the FalloutPref.ini & SkyrimPref.ini files to total disable shadows and lower some other settings that can only be done in the ini files. I also downloaded some mods to lower texture quality to improve performance and a few other performance tweaks as well. I probably played those games for an hour or...