As you wrote the two fleets were closely matched on paper - if anything the French probably held the advantage in material. But there’s no comparison in the British and French leadership. The French were still trying to operate under an outmoded system of centralized command. The British had developed a system of advising its individual ship commanders of the broad outline of the plan and then letting each one take the actions in battle that they thought best advanced that plan. And because the British fleet spend most of its time at sea while most of the continental fleets stayed in port, British officers and crews were much more experienced than their counterparts. As a result, British fleets repeatedly showed an ability to defeat the fleets of other nations, even when faced against a numerical disadvanatage. Look at Trafalgar: 27 British ships of the line against 33 French and Spanish - the French and Spanish lost 22 ships and ten times as many men as the British did. Cape Finistere: 15 British versus 20 French and Spanish - a British victory. The First of June: 25 British versus 26 French - a British vicotry.
Yes, I certainly don’t deny that a RN 74 was more than a match for French one. What I’m saying is that it’s not all that likely that the battle between Nelson’s fleet and Bruey’s would have been as lopsided had it occured at sea. A result similar to Cape Finisterre or the Glorious First would have been more likely, with most of the French fleet surviving intact. I think that the suggestion that had the fleets made contact in the Med, it’s likely that Napoleon would have been killed to be unfounded. Possible, sure, but particularly likely? No. Villeneuve survived Cape Finisterre and Trafalgar. Villaret-Joyeuse survived the Glorious First. Why should we think that Napoleon would most likely have been killed in this hypothetical battle?
Huh. That’s also the plot (except leaving the main engagement) of the final part of Patrick O’Brian’s Post Captain, the second Aubrey/Maturin novel. Damn those novelists using actual history for their plots!
Oh yes.
The capture of the frigate El Gamo by Thomas Cochrane’s sloopy Speedy was used by both authors.
IIRC, it was a French frigate, and the concern was that it would slip past the British ships and warn the Spanish fleet of what was about to happen, thus denying the British the element of surprise.
Maybe there’s a lot I don’t know about this, but I was under the impression that RickJay’s answer is the most correct one: that there were very few battles in the open seas before the 20th century (hence the practice of naming naval battles after the closest point of land makes a lot of sense).
IIRC, there was one very unusual sea battle that took place as far as 400 miles from the closest point of land (St. Vincent, maybe? 
). Do any of the folks positing other mechanisms for fleets finding each other in the 18th and 19th centuries have examples of naval battles of the era that took place on the open ocean (off the continental shelves? more than 200 miles from land?).
Just as an aside, standing even on top of a very tall mast really doesn’t take into account the sheer size of the oceans, as SteveMB has noted.
A good point. I guess I exaggerated the possibility of Napoleon’s death for effect.
Well, Stephen Maturin could hope. 
Maturin hadn’t even met Aubrey at the time. Aubrey was actually at the Battle of the Nile, serving on board the Leander, the little 50 I mentioned above. Or so his backstory goes. O’Brien then goes on to give Aubrey a cruise identical in virtually every respect to the first cruise of Thomas Cochrane, right down to incredibly minor details. There’s almost nothing original in the first Aubrey book. I haven’t read any others, so I don’t know how bad they are in that regard.
Maturin hated Napoleon before he met Aubrey, I believe.
Well, he would have made a pretty small target. 
Sailboat
Absolutely right. I don’t have my copy of John Keegan’s The Price of Admiralty handy at the moment, but he makes the point that in all of what I’ll call “the square-riggers-with-cannon period” of sailing-ship history only two battles took place significantly far from land. IIRC, The Glorious First of June, and Cape Finisterre (one of three battles by that name).
All the rest were “littoral” battles, either near land or in chokepoints like the English Channel.
Mid-oceanic military encounters are pretty rare in human history, frankly, and most of those would have been in World War II.
Sailboat
You have to admit, Napoleon vs Nelson would have been one cool battle.
I remember I once had an old SPI wargame about one of Napoleon’s early battles (Marengo maybe?). One of the features of the game was that the various generals had counters that you could use in the battle. But this exposed them to enemy gunfire and possible death. So if one of your generals was killed, you flipped over the counter and on the other side was a lesser ranked officer who was supposedly taking the genral’s place on the battlefield. The one exception was Napoleon; he had a counter and could appear on the battlefield but if he was killed and you flipped over his counter all it said was “Mon Dieu!”
Ah, thanks Sailboat, I thought I was going crazy…