Here is a list of important differences between warships in the 1570s, Spanish Galleons in particular, with those 225 years later. As you can expect, there were a lot of improvements in two centuries.

1. Built for Trade vs. Built for war. A Spanish Galleon was a fighting ship only incidentally, it was mainly built for trade and transport. A British or French 74 gun ship of the line would have been purpose built for war.

2. Size. 200-600 tons burden vs. ~1600 tons. Although similar in length, a 74 from the 1790s would be at least three or four times as large in bulk and carry twice as many men.

3. Sailing Qualities/Speed. Although Galleons were a large improvement on earlier designs, by the 1790s hull designs and sail plans had improved to make ships of similar sizes much more weatherly and resistant to storms, A fleet of 74s would not have found the voyage of the Spanish Armada to be particularly trying or damaging although they were still at the mercy of winds and tides. In practice, being more weatherly and seaworthy would also make them faster and more maneuverable when employed in a group. A ship that can sail a bit further into the wind that its adversaries has the power to leave fights at will and often pick them.

4. Guns and firepower. A Spanish galleon would have no more than 12 or so guns throwing 9 pound balls or smaller. These would have a slow rate of fire, perhaps a shot every 5 minutes Day (edit: this was a bad error on my part), and use uncorned powder, which is much less powerful. A 74 gun ship of the line had... wait for it... 74 guns (edit: approximiately 74 but freqently more), which were mostly 24 or 36 pounders. A very well trained ship could fire three rounds per gun in 5 minutes. As a consequence, Galleons mostly relied on boarding actions, while the later ships had evolved to use their firepower to cripple enemy ships.

Hi, thanks for the PM -- I have answered similar questions to this one a couple times in the past:

http://www.reddit.com/r/AskHistorians/comments/2709jm/how_would_a_britishhms_frigate_built_in_1715/

This one in particular would be useful to you:

http://www.reddit.com/r/AskHistorians/comments/20x9kz/classes_of_vessels_during_the_age_of_sail/

Very briefly, so this isn't just a copy pasta of that answer:

• A ship of the line would be fully square-rigged by the 1790s (that is, it would carry square sails on all three masts); galleons generally carried a lateen course (mainsail) on the mizenmast and sometimes a lateen course on the mainmast and/or foremast. The square-rigged ship might carry a gaff mizen course (sometimes called a spanker), but it would be rigged on a gaff yard. (You can see this evolution on HMS Victory -- although as first commissioned it carried a lateen mizen yard, it only carried a spanker on that yard; in its "current" rig it's a gaff mizen course.) The "modern" ship of the line of the Napoleonic period would carry topmasts above the mizen mast; the galleon wouldn't be likely to do that.

• A ship of the line would have a much greater length-to-width ratio than a galleon, and wouldn't be built up as much above its top gun deck. A distinguishing feature of the galleon was its large "castles" on the front and back of the ship, which you can see here in a modern painting and a contemporary illustration of the Mary Rose. These were useful for boarding and for carrying guns higher in the ship, but they compromised the ship's handling and its stability.

• A ship of the line carried its guns almost exclusively on the broadside, and aimed them on the broadside. In the image above from the Mary Rose from the Anthony Roll, you can see that its guns are pointed forward, which reflected the tactics of the time -- at least in the English navy around the time of the Armada, ships would take turns sailing down at another enemy ship, discharging guns as they bore, then withdrawing to reload. By the Napoleonic period (though starting in the mid-15th century), the dominant tactical paradigm would be to form ships in a line ahead (that is, in a single line ahead and astern of one another) to present a unified line of guns to the enemy. It also became the norm to attempt to deliver a unified broadside from a single ship, at least when firing commenced. Finally, broadside tactics also led to an increase in desired speed of reloading -- we know that some of the Spanish ships fighting the Armada only fired one or two shots per gun per day, and in the Napoleonic period the perceived paradigm for fighting efficiency was three broadsides in five minutes (though this was exhausting to keep up for very long). The major difference was in using gun carriages that allowed for recoil, which meant that guns could be reloaded inside the ship -- far easier to do in an engagement than reloading using stages over the side of the ship.

It's also worth pointing out that "galleon" and "ship of the line" are both broad concepts -- a ship of the line could carry anywhere between 40 and 140 guns, and galleons were built in several countries to a variety of sizes with different intended roles at different time periods. Still, I think the above is a fair overview; please feel free to follow up with questions.

edit: fixed a time reference; not enough coffee yet