To simplify, the differences are similar to comparing a dart to a glider -- it all gets back to the wings.
The delta wing provides the best overall flight characteristics in terms of lift and control surface efficiency. A delta wing will allow you to come in low and slow and in control, but is that always what you need if you are flying a fighter jet?
The aerodynamics of fighter jets are designed to provide lift, stability, and control at a much wider angle of attack. Comparing the wing characteristics between the two planes in a wind tunnel, notice how the wing thickness (airfoil) of the fighter plane is much less (relatively flat) at the leading edge.
Although the fighter plane provides less lift at the same angle of attack and requires a faster airspeed to stay aloft without stalling, the control over a wider range of airspeeds is worth the tradeoff for the fighter jet performance and maneuverability.
Shut down a fighter plane engine, and it will drop like a yard dart. The intake on a fighter plane is designed to receive as much air as possible, and will cause turbulence at the inlet if the blades are not turning fast enough. There simply is a minimum speed range to keep the plane in flight and under control as it is coming in for a landing.
The power to weight issue has a downside -- the fighter plane is less efficient in fuel consumption -- it is even less efficient if the inlet has nacelles or ducting to mask a thermal signature.
The power to weight ratio of the fighter plane is much higher than a commercial aircraft, and the answers above from the other posters regarding thrust cover the topic well.
The best fighter jets provide the most maneuverability over the widest range of speeds.
Both types of aircraft would technically benefit from a lower landing (and stalling) speed, but in both cases, other flight characteristics are a higher priority.