Going from memory here, one of the FDEVs said that the increase in pips isn't linear. There is a slight curve upwards in effectiveness, so the 4th pip is a little better than twice as good as the 2nd pip.
They also confirmed that SYS does affect shield strength, with the 4th pip in shields being noticeably better. That's why I always have 4 pips in shields while docking.
More pips to Engines increases top speed and also tightens your turn rate. More pips to Weapons increases cooling (available firing time). So in combat I'm constantly switching.... pips to engines when chasing, then switch over to weapons for a longer firing burst when I'm in range. Then back to engines if the bandit evades, and over to shields if I'm expecting a head-on jousting approach from the bandit. That also
might save you if you're rammed, although relative hull size and weight still matters.
In a completely asymmetric fight, where your ship badly outclasses the enemy ship, you don't have to do all that switching back and forth. But it comes in handy if you're taking on big game in a light fighter that isn't fully upgraded.