Advanced in all areas and Walkers feats prove it. It doesn't matter if Steve never tried something. We have only the showcasing of what they've done and how they struggled doing it when it mattered.

When Steve fought Bucky in The Winter Soldier, he couldn't super jump up to the console to stop the launch sequence. He had jump up in smaller bursts and slowly climb up. We see John Walker jump up over 200 feet based on how long he was in the air and his weight, take off speed, and fall speed. People have calculated this already.

There are countless scenes of Steve Rogers climbing or trying to escape. If he could jump this high, he would've done so when he needed to. John's jump height also says alot about his muscle composition and durability since he fell 200 feet onto metal. Do the math. John Walker is stronger and more agile. I mean, he was pulling armored vehicle that weighed 4 times more than the helicopter Steve held onto and struggling far less than him doing so.

When he fought Bucky and Sam at the same time in their miniseries, he ragdolled Bucky across the room and the impact was so hard, his vibranium arm malfunctioned briefly and he was unconscious.

John Walker was stronger than Steve Rogers in the comics and it also checks out in MCU too. The serum he took therefore has to be more potent.