Attack values

It depends on your Pokemon's level. The 15 Attack IV Machamp will hit its breakpoints half a level before the other one, and its charge move will do slightly more damage.

Powering up 1/2 a level extra per point below 15 attack is a good rule of thumb.

As others have said, it's generally a difference of half a level, or a single powerup.

To give an actual example, a 15A Machamp will hit the breakpoint against Dialga at level 36. A 14A needs to be level 36.5.

It's going to be rare that you'll find a situation where a 14A (or even a 13A) can't reach the same breakpoints as a 15A, provided you're prepared to spend the dust on it. If the specimen is good in other areas (other IVs, high level), then I wouldn't necessarily rule it out.

As others have said, breakpoints mean that you will usually just have to power up a 14 attack pokemon one more time to deal the same damage.

GP has a more comprehensive guide on breakpoints here: https://pokemongo.gamepress.gg/guide-breakpoints