It's really annoying that such records of the time that exist had no regard for future wargamers.
We have really poor information about how these ships were fitted out. If anyone has a link or two I would love to see them, since I have some cog ideas flitting about my head. In the meantime, we can work with this:
1) There were few purpose-built warships. Most were commandeered merchant ships. They threw the platforms on and that was that. The few that were built by the nobility to give them standing naval capability weren't constructed any differently that merchant cogs. Since ships were called up for battle and then returned to commercial work they might be outfitted differently from one season to the next. So there is no Jane's, no Anthony Roll, nothing. You call up all the men and ships you can and have at it. No way to run a railroad.
2) The engines probably didn't make a big difference. I believe this because when one element of a force makes a disproportionate impact, like cannon, hoplites, cavalry, armored divisions, etc, the records make a point of mentioning numbers. What we have doesn't mention the big weapons with any emphasis, so I conclude that they were nice to have by didn't make the difference that a six pounder made to a company of regulars in the French and Indian Wars.
3) When they had guns they probably used them shotgun style – load them with bits and fire at close range. They wouldn't have been very good at range even if the hull shape and rigging of cogs didn't make them poor firing platforms. I bet in practice the longbows had a better range than the guns. Guns are still scary, though, and if fired right before boarding they do a lot for moral and make things easier for boarders.
Constantinople was different. They anticipated and prepared for assaulting walls. I don't think those ships were typical. But then, everything was ad hoc anyway.