All else being equal - and that is usually not the case, because it depends on the exact tip design and material, the headphone more than you'd think, and mostly on the physiology of the user which can greatly affect the fit and seal, all of which is why impressions and opinions vary and conflict - the effect is generally considered to be a subtle increase in higher frequencies (say, > ~5kHz) for wider bore silicone tips. Some tips, like comply foams and spin-fits, have been measured to slightly reduce those frequencies. But again, all is not equal; I tend to perceive spiral dot tips as having more bass than other wide bore tips, and that's probably because they seal better for me.
But for (competitive) gaming, what you want is precision; accurate transient response and timing of left/right sounds. The exact frequency balance matters less, although overblown bass tends to cloud detail - but the E80 certainly doesn't have that problem (in fact I don't use mine because I simply like more bass in my music, but then I never used it for gaming or outputting from a console). What you should do, is pick the tip that makes these small sounds, and changes in sounds, most audible to you. Could be higher frequency detail you want, could be lower frequency fundamentals of sounds for footsteps and the like. Ultimately, again, the effect is subtle, so as nuke says long-term comfort will likely end up the biggest factor.
