Doyler - Apologies for the harsh post, I was in a very bad mood and let it come out in my writing, hope I can correct things below.
Braking on a road bike - as others have said, you seem to have been struggling with small hands vs long reach, a not uncommon problem.
Firstly, the set up. I suspect your brothers bike was too large for you, add to that the poorly designed Sora levers, and what I suspect to be poorly set up bars and it isn't surprising you struggled.
Discount your experience on his bike, it is your bike that matters. When chosing bars for your bike, it is recommended for small hands to use a shallow drop bar, as opposed to a deep drop. I find the Easton EC70 to be exceptional in this department, and the 3T Morphe are held in high regard too. Also consider women specific bars, as they are designed with small hands in mind.
One thing to look out for when buying bars, if you struggle to get a comfortable reach to the levers is the width, bars are often sold to customers being too wide, which alters your wrist position and makes it harder to grasp the levers from in the drops. The bar should be no wider than your AC bones (the bumpy bit at the edge of your shoulders) and it is good practice to go for the bars with a width the next size smaller than the width of your AC. Hold the bars up to your shoulders and see if they touch your AC or not.
Pad travel and pad compound. Smaller hands need the levers closer to the bars to exert good, modulated pressure on them. You only need a fingers space between the lever and the bar when at maximum pressure, so you don't trap your outside 2 fingers in an e-stop. This gives you better modulation over braking pressure, but it is adviseable to use very soft pads to get the most out of your brakes. KoolStop Salmon are absolutely top notch for this.
Lever position. Where your brake levers sit on the bars is an exercise in practice, and involves both rotating the bars in the stem to find the most comfortable slope angle, and moving the levers up and down to find the best trade off between hood comfort and brake reach in the drops. I personally chose to sacrifice a bit of hood comfort for easy reach in the drops, as that is where I go when maximum braking control is required. i.e. filtering, approaching junctions, and of course descents.
Brake application. How you brake makes a bigger difference to how they perform than you might at first think. Squeeze on the brake, and as you feel pressure build in your elbows, apply more pressure gradually. This way you will get maximum performance, safely.
Gears. Roadbike gears are far superior to mtb gears once you get used to them (for on road use that is). You will get used to using them to keep your cadence high, and will wonder how you rode an mtb efficiently on the road before. Get used to shifting down 1 or 2 on the rear for an upshift of the front, and up 1 or 2 on the rear for a downshift of the front - it smooths the transition.
Acceleration. His bike could have felt sluggish for lots of reasons, but it was likely down to his tyres and your muscles not used to putting the power down on the road. MTB posture and road posture work your legs differently. It will also partly be down to the bike - yours will feel like greased lightning, even before you get your road muscles.
Tyres. Just a quick pointer - Michelin Pro2 / Pro3 Race tyres are the proof that there is a god, and that he is a cyclist. Those tyres are seriously the head honcho of the tyre world. Don't just pump them up to the max either, experiment (and write down!) different pressures and you will come across a sweet feeling set of pressures. Front and rear do not have to be the same pressure. I have 700x25c P2Rs and weigh 75kgs, the sweet spot for me is 6.5bar rear 5bar front.
HTH
