The headlight relay mod is just a band aid, used to side step and hide faulty wiring harness connectors and switches. It only solves a small portion of the real problem
Check the voltage across the battery compared to the voltage at the headlight. The voltage disparity is what the harness terminals and switch are tossing into the air as heat, which is just wasted energy better used to keep the battery charged.
Improving the voltage to the headlight will certainly make it brighter, whatever headlight you have. The watt ratings for headlights are made at 12.8V. A 50 Watt bulb is only consuming 30 Watts if fed 10V, for example. A headlight intended to draw more watts, will make the voltage loss in faulty circuits worse, and it will never attain it's rated wattage or brightness expectation.
Worse, your 550 doesn't have a lot of alternator power to spare for more watts consumed by harness bits, switches and a headlight that consumes more power, particularly when compared to the 750.
The 550 alternator is rated for 150 watts at 5000 RPM, it only makes about 40-50 watts at idle (which is barely enough to light the headlight forget the about the coils, alternator and any other lighting loads the bike has). A stock bike with the headlight on, draws about 120-130 watts. Your battery depletes at idle with the stock components and will do so faster with a headlight that consumes more power. Further, the RPM point at which the battery begins to receive a charge gets higher, as it has to overcome the added headlight drain before it can charge the battery. And then, with engine revving, the power that would normally recharge the battery, is siphoned off to the headlight instead. The effect of which is that it is very hard to keep the battery in a well charged state, and the increase state level changes shorten battery life.
Finally, and few people seem to care about this, headlights don't throw a round light pattern. It's kind of sideways keyhole shaped. And, the reflector pattern for motorcycles is shaped differently than automotive light patterns so as to minimize light reaching oncoming drivers eyes. There are many who simply don't care about other drivers ability to see on a dark night, and are unconcerned about anything other than themselves and what "looks" good to them. However, I do question the "wisdom" of making oncoming vehicle drivers blind. But, for some, making other people pay for your life decisions is what makes living worthwhile, I imagine.
Do the voltage loss test first and correct that problem, if found. You might find out that your "weak" headlight works pretty good when fed its rated voltage (or above, if the battery is being charged nearer to 14.5V).
Cheers,