Engineers serve two purposes. They most obviously increase speed, but every ship has its speed cap and some can be quite easy to reach, some not as much. Good engine ability helps with this, but it is generally more valued for the impact on overheat duration. More engine ability means longer OH times and there is no limit to how long you can OH for, only limits on how much ability your engineers can have.
An RN Engi, properly classed, boosted with max vets (rounded down to 360) and max experts gains 290,000 TA for every +1 growth. So an Elite Engi (+13) would have 580,000 more engine ability than a +11.
Overheat time increases by 1 second for every 110,000 engine ability, so with an extra 290,000 on 7 engineers would work out as an extra 18 seconds in total. Bear in mind, this was the amount of OH time gained for every +1 ability on an RN engi with a boost, max vets (360) and max experts.
And that's the maximum potential difference between an engi with +10, +11, +12 or +13 engine. Obviously the amount of extra time you get from your engi will depend on your vets.