My induction hob can heat things up faster than gas

It's a combination of high power and high efficiency

Or do I just have a really weak electric stove?

I think you might just have a really weak one, or poor compatibility pots? I've had both, and if anything my gas burners feel a little slower and cooler than my induction stove did.

An induction stove with booster can outheat any gas stove.

Our induction plate rivals the power of the electric range in this apartment. Our previous induction plates were on par with our gas stove. Am hoping for even more power when I upgrade to a built in induction range that’s wired into 240v.

I found if the pot makes solid contact with the electric elements the electric can actually heat up water faster than gas. But if the bottom of your pan isn't flat or the element is warped, they are really, really, really slow.

My experience has been with gas (fast), electric resistive with exposed and warped elements (slow), electric resistive with a glass top (fastest).