In general, very little. Charged moves will be slightly higher damage at 15 atk, but that will likely equate to a few seconds at most on a raid.
Where it DOES matter is with quick attacks. Quick attacks always do full points of damage (so like 5 dmg will go to 6 after you've leveled a pokemon enough, never 5.5) so after a Pokemon is raised so far, they will hit a "breakpoint", which is a point where the Pokemon's attack stat is high enough for it to deal 1 more dmg to a specific target with its quick attack. Higher attack pokemon see these breakpoints sooner, and it IS possible to have a low enough attack stat to miss a breakpoint entirely.
As an example, let's look at my personal Kyoger (14/15/15) VS a future Entei raid using the breakpoint calculator found here:
https://pokemongo.gamepress.gg/breakpoint-calculator#/
So entering Kyogre as the attacker and Entei as the raid, you can see the DMG done to Entei at each level for each damage point. For example: at LV33, Waterfall goes from 19 DMG to 20 DMG per use, which makes a fair difference considering how much you use quick moves! But since my Kyogre has 14 attack, it needs to be 33.5 to hit that break-point. Generally speaking, 1 point in attack=1 more power-up to hit a break-point.
But hold on, let's look again; that's not the last break-point for Entei! If you look, at the VERY top corner, there's one final break-point at LV40... one that my Kyogre BARELY misses by having only 14 attack! And this is why 15 attack is so valued among many trainers; you get break-points earlier, and you never miss a break-point. What does that mean for me? Almost nothing. My Kyogre is only 35 atm and this scenario ONLY works with Entei. If I switch the raid-boss to Moltres or Golem or any other boss, the breakpoints are entirely different. And chances are there will never be another raid-boss that my Kyogre will miss that final break-point on. At least one that I'd use it against! Pretty much, it's just a question of what your 'mon is fighting and how high you want it leveled.
Note that this is based on the target, as every Pokemon has its own types and defense stat, and fast-paced moves like Shadow Claw see a larger boost from this than slow yet powerful moves like Waterfall.
Most players tend to value attack above other stats, but don't sweat over it TOO much.
