IV Breeding gives you an edge in Wifi and Competitive battling. It is however, basically neglectable in normal Ingame teams - waste of time really. Lets take an example;
Level 100 Alakazam, 252 EVs on Special Attack;
338 Special attack with 0 IVs
369 Special Attack with 31 IVs.
So the range is 31 of the possible different stats. So, in such an extreme circumstance, it's actually quite a bit as 31 points on one stat is quite significant. However, EV training > IV breeding imo. While IV Breeding gives you an edge that can potentially win you the match, no the difference is not all huge in most cases. However, it is advisable if you have the time to do it.