The power used (more is better)
The distance from the emitter (less is better)
The curvature of the shield (more is better - which implies smaller)
A BIG punch
People said this earlier. A fighter sacrifices protection and, IMO, power. Like Mark Olson said in his answer, the whole point of a fighter is dealing a good punch in a quick way. Capital ships, on the other hand, have to be durable - they house smaller ships, machinery and a ton of people! If you ask me, these ships should have a generator that compares to 50 fighters in size alone. They have to capitalize (ha!) big time in the point 1 of your three statements.
A fighter's generator will use points 2 and 3 in his favour in order not to need such an enormous generator. Think of this as two people going from point A to point B. Capital has a motorcycle while Figher has a bycicle. Instead of trying to motorize the bycicle, the Fighter will just find a street with a steep slope to go faster. It might not be as fast as a motorcycle, but it will definitely be faster and less tiresome.
They also need to deal high amounts of damage. In order to create a blast capable of piercing through equally or even stronger shields, these ships need a lot of power (IMO, most of the generator's power). So they save all that energy to the blasts (that might be as powerful as those of the big guns from capital ships) while using points 2 and 3 as engineering advantages, "perks", to ensure good shields with smaller amounts of power.
Different kinds of projectiles
Since you like games, I'd recommend you play FTL: Faster Than Light. It's an amazing game and they use this concept perfectly.
Your shields are about protecting the ship from damage - but who's to say they're effective against EVERY kind of damage?
In FTL there are a few types of weapons but we can narrow them down to, basically, two kinds: Lasers and Missiles. Shields are only effective against lasers. They deal no damage whatsoever to a ship with shields up. A missile, however, will pass straight through the shields, damaging the hull instantly if it hits - and this is why maneuverability is important in this game.
Alright. The Fighter's shields are, indeed, stronger than the capital ship's. But for how long?
Keeping the shields up while powering a Figher AND dealing a big punch might be too much for a small generator. With this in mind, maybe these shields could be completely situational.
Think of the X-Wings in Star Wars. Every pilot is in company of a droid that aids him in battle. Maybe this droid is able to make decisions in real time and selectively activate the shields when needed - although the pilot can have full autonomy to bring the shields up whenever he wants.
Maybe they can only be up for small amounts of time, in order not to affect the other systems of the fighter. After each use, they have a cooldown time while the generator stores enough energy for another use.
It's also a good mechanic for your game, since all you have to do is put in a cooldown counter.