As Little Nemo noted they are the antitheist of each other. H. from humble background, A the son of rank (his father was a general in the army and A fell heir to a considerable estate), H a thinker and master of the indirect approach, A sort of a bull-in-the-china-shop and inclined to impetuosity, A satyr and lady killer, H trapped in a loveless marriage and filled with guilt over his affair with the Duke of Wellington’s sister, A lusting for fame, H just looking to live with himself, A big and boisterous and probably a borderline alcoholic and glutton, H abstemious and retiring, H a loner and A with a wide circle of friends and a dear companion in M (all H. had was Bush and that was always a superior-subordinate relationship although caring), H intellectual and A instinctive. Two different guys. Both very good officers but very different people. Both great fictional characters.
Amusingly for complete opposites, allegedly the exploits of both were inspired/based on the same guy - the real-life Lord Cochrane. 
There’s nothing allegedly about it. I read most of the Hornblower books a long while back. A few years ago I read the first Aubrey book. Enjoyed it. Shortly after that I started reading a biography of Cochrane. The man’s first independent cruise was point for point identical to the plot of the first Aubrey book - got that little brigantine or whatever it was, tried on some large cannons, took them off because they threw the sailing qualities off, captured various enemy ships in the exact sequence as Aubrey, ran away from the enemy ship of the line throwing everything overboard to do it, capturing that odd Spanish gunboat (right down to the doctor at the wheel on that one) - it got so that there was no sense of discovering Cochrane’s life story because I knew what was going to happen next. The only parts of that book that O’Brien actually came up with independently were the character of Mathurin, the first officer’s intrigue with the Irish, and Aubrey’s affair with the wife of his superior (irl Cochrane had a feud with the same admiral for different reasons).
Turned me right off from reading the rest of the series, which is probably a shame given that everyone raves about them.
I always recommend that people start reading Aubrey/Maturin with “Post Captain”, not “Master and Commander”. That’s when O’Brian really gets a feel for how the series will go. All the same, I understand that a lot of the battles are pretty much shot by shot replays of real ones.
The big difference is that O’Brian uses a page when Forester would use a paragraph. I enjoy them both mind you, but Hornblower is better written.
I think Ioan Gruffudd is better looking than Russell Crowe.
(I’m about halfway through the Aubrey/Maturin series right now–I just finished The Ionian Mission–and only skimmed a bit of a Forrester novel once. So far, O’Brian’s books are hilarious and hugely compulsive reading, while the little bit of prose I read in the Hornblower book was very dry and starchy. But I’ll come back when I know more.)
I say “allegedly” because there is more doubt in the case of Hornblower. 
“Bizarro Hornblower”: damn, now I wish I could use that for a screen name.
Nitpick: while he was consumed with guilt over his infatuation with Lady Barbara Wellesley (and envious of her marriage ot an incompentent superior), he did not have an affair with her. He did have an affair with, Marie, the daughter in law of the Comte de Graçay, but he left her as he, a peg-legged Bush, and sailing master Brown escaped down the Seine, stole the cutter Witch of Endor under the noses of the French, blasts two pursuing craft, and sails to the British fleet and then across the Channel to what he believes to be almost certain court-martial and the arms of his fatuous wife, Maria. (It’s hard to tell which is the worst fate.) However, publicity and death in childberth respectively have by improbable fortune freed him from his fate and marriage, and leaves him at loose ends to engage the now-widowed Lady Barbara–minding his offspring–in romance.
Aubrey is dashing and bold, but also prone to overreaching and making errors. Hornblower is a man who thinks through his problems, is very aware of his personal deficiencies, and takes well-calculated risks. He’s also accounted with unnaturally good fortune, which he almost always makes the best of. In a mono y mono fight Aubrey could take Hornblower, but as sea captains in command of comperable fighting vessels I’d give the edge to Hornblower any day of the week.
Stranger
C.S. Forester has it in for his heros, and awful things frequently happen to characters in his books. Hornblower is one of the most conspicuous of the Forester heros who gets away with it and comes to happy endings. This may have something to do with why they’re the most popular of his books. There have been a few other lucky Forester characters (The Captain From Connecticut), but Hornblower has been, overall, the luckiest, with the biggest series.
I don’t buy that he’d lose against Aubrey in one-on-one. Hornblower has shown himself pretty capable in personal combat as well as command, and his rationalism is not obviously a handicap against an emotional opponent.
Don’t forget … he later has an affair again with Marie, when feeling slighted by his now-wife Lady Barbara hosting at the embassy.
Forester promoted his hero rather too quickly for character development (but then he didn’t write them in chronological order and probably didn’t bank on them becoming so successful) and there are one or two problems with the internal consistency of the timeline.
Who has seniority? Was Aubrey a Captain w/o command during the same dreaded peace when Hornblower was a lieutenant supporting himself playing whist?
My thread might have a problem here, since the winner would face a court matial for striking a fellow officer. 
As best I can determine, this is about captains in books, right?
Moved from IMHO to CS.
“I’m a dead man, Stephen.”
“Shh, honey, what is it?”
“I called out that fellow Hornblower, and like an ass, I let him choose the weapons.”
“Mary and Joseph, brother, fear not, I can tutor you in all the weapons of the duel. What did he call for, the rascal? Pistols? Rapiers? Sabres?”
“You don’t understand, Stephen. He called for moping at ten paces!”
Stranger, I’m not disagreeing with what you said, but I have to correct one thing. The phrase is “mano a mano,” referring to hand-to-hand combat. “Mono y mono” would be a “monkey and monkey” fight. While not entirely inappropriate for a Georgian naval battle, it does put an entirely different spin on guerilla warfare.
If the contest was who you’d rather hang out with, then my vote is for Aubrey. Unfortunately, since I’m female, he’d probably stick his foot in his mouth and then be insulted because I was busy giggling at him.
Ladies and Gentlemen, we have a winner.
Now, now, Miss McKnittington, you can’t have your chickens and eat them, too.
Rather, what I meant was, a cake in the hand is worth two in the oven…no, hellfire…er, darn me…
“Oh Jack! You can debauch my sloth any day. . .”
Pah, I say! Pah! We would eat amusingly-named boiled puddings, discuss music, and he would make a fool of himself attempting to compliment me. Besides, I don’t own a sloth.
[sub]I could never wrest him away from Maturin, anyway.[/sub]
Was Jack Aubrey ever emotional in a battle? Ashore, certainly - but in combat he seems the essence of a cool, rational commander.