How did the armies of the Bahamanis, Ming China, and Morocco compare to the armies of England, Spain, and the Ottoman Empire during this period? Was the Ottoman success against the Arab states facilitated by their European technology?
The Imjin war was a good measure of what was available at the time. The Japanese had an advantage from muskets on land, but the Koreans gained decisive victories on the water from naval artillery. They were fortunately able to dual-purpose the same A-class cannon on water and land, since their ships were heavy enough to mount them. These cannon had ranges over 1 km, while the Japanese only had musket fire.
The Koreans also had a land victory in a siege at Haengju where they were able to rake attackers with fire from multiple rocket launchers and cannon, although much of their fire was arrows.
The Japanese apparently valued their musketeers so much that they gave them extra rations during a siege; it's clear that gunpowder played a critical role on both sides.
YI find this question very difficult to tackle directly because on one hand we can compare these nations in a hypothetical what-if any two of them were in a stand-out fight plus minus some caveats as to what is realistic or not (how big are the armies? How much experience? How good the logistics?). But that really goes into historical what-if that I personally prefer to avoid.
But some of the facts are this.
Bahamanians were at severe disadvantage even fighting in their own turf, let alone elsewhere.
Spanish troops could beat Morrocans in North Africa barring bad weather, but holding on to those fortified forts or presidios was another matter entirely. Their adversaries had every advantage fighting an irregular warfare in their home turf so over time all the presidios were lost except for several that are easy to reinforce.
The Ottomans were stopped in their westward advance due to a combination of inability to project farther west in the Mediterranean due to Malta and Lepanto, and over-stretch of their supply lines on land. European climate and terrain limited their campaigning range and time.
After the Spanish established their outpuost in the Philippines, their contact with China convinced them that they only needed a small army to defeat all of China. Plans were drawn up, only to be scrapped as they needed to focus on other threats nearby (Ottomans, England, wily Dutchmen).
Essentially I have a hard time and I do not think that "firepower" can be defined in a vacuum.