It is a yes and no answer; first understand a little about what fuel injection is. All diesel engines use fuel injection and always have, modern cars do but have only used some type of direct injection for about 20 years. Benefits of fuel injection include smoother and more consistent transient throttle response, such as during quick throttle transitions, easier cold starting, more accurate adjustment to account for extremes of ambient temperatures and changes in air pressure, more stable idling, decreased maintenance needs, and better fuel efficiency.
Gas is different then diesel; gas injection took off with computers. What happens is the computer monitors the amount of air going in to the engine from the mass flow air sensor. The  computer then decides how much fuel to inject. This is where you get fuel economy, instead of just dumping fuel when you step down it controls the amount of fuel. The engine can only burn so much fuel if you put more fuel in then your engine can burn it is just waste and go's out the exhaust. This is pollution, and hurts your MPG's. The computer controls the amount of fuel with the amount of time the injector opens.
For gas; just putting bigger injectors won't help much. If you put a injector that is to big on it will hurt. What happens is the computer monitors the air and then shortens the amount of time the injectors open. Your engine will become more efficient with a injectors that is a little bigger, it dose this by putting more fuel in a shorter amount of time and a little horsepower can be gained. If do a tune you can gain more horsepower. This is done from adjusting the computer so your engine will burn more fuel. You could hurt your MPG's and can run in to problems with emissions but will gain more horsepower.
Diesel injectors worked off a a injector pump. Older diesel had mechanically driven pump. It was timed with gears or a belt off of the crankshaft and camshaft. Just putting bigger injectors would increase horsepower because the amount of time the injectors opens was not controlled a computer. Most of the time the timing has to be advanced to work better. If you go to big it will create a lot of smoke, smoke is unburned fuel.

Will installing bigger fuel injectors give more horsepower?

Understanding fuel injectors

It is a yes and no answer, injectors and horsepower

Diesel today still have a injector pump that is driven off the crankshaft and camshaft with gears or belts. The injection is controlled from a computer it dose not have a mass flow air sensor but uses different ways to tell the injector how much fuel to put in the cylinder. Just installing bigger injector on this type will increase horsepower but there is limits. Most of the time a boost fooler is needed to trick the computer so it will add more fuel. A tuner is needed to make full use of the bigger injectors.
Bigger injectors on diesel can give better fuel economy. There is a balance on how big and where your foot is. I have a 01 Dodge cummins, I have a lot of upgrades and had 175 HP injectors on it. It ran good but made a lot of smoke. I do a lot of city driving and it was almost hard to drive without dumping smoke. I towed about 10,000 pounds form Maryland to Texas and stayed around 15 - 16 MPG's I did not see much difference when not towing .  I went with a smaller injector just for driveability and the next time I towed I got 13 -14 MPG's.
I hope this helps someone on their decision on getting bigger injectors. The best thing to do is call a injector dealer and tell them what you are looking to do. I did this and was told that 175 HP injectors on my truck might make smoke but I gave it a try any way. I sometimes think about putting them back on. I tow a lot and like the fuel economy, but have to decide what I want something easy to drive or fuel economy.
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