Frankly I fail to understand why two stations with the same wattage should perform significantly different if we just compare the ability to melt solder.
The way I look at it:
1.
Power rating may be "generous" on some clone devices. For instance, when Hakko 888 is stated to have 80W, it is not overstated. If you calculate the resistance of the heater, as it is when at working temp, and the voltage from the PSU once the transformer is warm and under load, it checks out. The clone station may be 80 watts peak when you first turn it on, cold, but it is not apples to apples. When the heater warms up and increases in resistance, the power drops. The transformer output sags under load and may drop a bit once fully warmed up. It's under these conditions where the Hakko 888 is measured from. Not the cold start conditions. (I use example of Hakko 888 because I have actually measured these things, and the transformer regulation is actually exceptional). IOW, the way you decide to rate the power of a soldering iron is not set in stone. There are many legitimate ways to describe the power rating, depending even on the temp of the iron. At say 480C, even Hakko 888 is not going to meet its power rating. The power output drops due to function of resistance vs temperature in the heating element.
2.
Power delivery/efficiency. Let's say power is actually equal.
A. Thermal loss to environment. You can't warm up an iron to 300C and then unplug it, wait 20 minutes, and make a joint. The iron is constantly transferring heat to the surrounding environment... largely by warming up the surrounding atmosphere through conduction and to surrounding PCB/bench/air through radiation. One iron will be a better heatsink... or a less efficient soldering iron.
B. Thermal path to the iron tip: Due to shape and construction of heater and tip, one will have a better transfer to the tip, and the tip is the closest you can get to the joint. On the less efficiently designed iron, areas other than the very end of the tip will reach higher temps than the more efficient one when the heater is on. This is "stealing" some of the wattage that gets delivered to the joint in the short run; and even once the entire iron has reached steady state (while you'll holding the iron to a massive joint/heatsink waiting for something to happen), the relatively higher temps of parts-other-than-the-end-of-tip increase the heatsinking to the surrounding air. See A.
So what wattage is there is not going to be delivered to the joint to the same degree. Another way of saying it is that given two irons of equivalent power, if you back out and consider the temp change of the entire room and its contents, they may be equivalent when putting out maximum power. But one of them will get more of that heat into the joint.
3. Thermal response: An iron can respond faster to temp change than another. This can make a significant difference in practical soldering and temp stability. But in the long run, maxed out steady state, no not really.