See I think the soldiers are actually, being a machine, a lot stronger than people think given its size. Specifically in the Meridian section we see a pair throw two armored humans out of their warthog well over 20 foot up into the air with one hand. Brutes, especially enraged brutes are very strong and they can easily pick up a marine and throw them a little bit but not that far. So the soldier is stronger than the brute. In CC it wouldn’t be as one sided as you would expect. Unless the Brute had a gravity hammer, he’d probably get rude shock if he tried to simply go berserk and overpower the Forerunner construct.
Also, the soldier can both teleport onto the battlefield, avoiding any AA, quickly traverse the battlefield and can also use it as a dodge ability. Generally they’re a lot faster. However, some brutes can take jetpacks to make them quicker. But not all Brute soldiers have this.
I’d say the suppressor and turret are about the same as the spiker and bruteshot. But the light rifle is one of the best heavy rifles in the game and would give them a major edge in a firefight against brutes with carbines.
Also, the Brutes normally go berserk once their shields and armour is gone. They then rely on their natural toughness and immunity to pain to shrug off shots; only dying when theres nothing left of them to fight. But, Promethean weapons disintegrate flesh on contact. So that advantage would be lost in a fight against the Prometheans as they have anti organic weapons for fighting Flood.
The biggest weakness the soldiers have is that they are extremely fragile, being easier to kill than elites or knights. This means that the brutes could essentially overwhelm the soldiers before their advantages in fire power and strength could come into play. Basically the soldier is a glass cannon.
So one versus one, the Brute would win because he can still kill the soldier before he himself will die; his armor able to absorb the ranged attacks long enough to take down the soldier. If he goes close quarters, the brute loses, if he goes berserk after his armor breaks, the brute loses.
In the wider story however, the soldier is an infinitely replaceable combat construct that can be churned out by the billion whereas an adult male brute trained to fight is a finite resource and experienced ones are irreplaceable.