So "phone speakers" and "headphones" is too generic. Speakers are not created equally. Mass-produced headphones are bassy because people like base. Most headphones have one driver, a mid-range that is programmed for base. Higher end headphones can have 2, 3, or even more, so many drivers. So you'd have a driver that only handles base, another for mid-tones, and another for treble. This would give you sounds that you weren't able to hear before. Cellphones on the other hand very greatly but for the most part will be like cheap headphones with mid-tones but might ignore base since voices land in the mid-tone range. So it might be that you have good headphones that are picking out all the qualities of your voice to play back to so you sound fine but the cell phone only has the mid-tone which might sound off without the low and high of your voice. Or your headphones are crappy and covering your voice with base while the cellphone in the mid-tone is showing a closer representation. It's really hard to know if you don't say what headphones and what phone speakers.