I am very interested in purchasing a game from the Patrician franchise but I'd really like to get just one. Which is classically consider the pinnacle of the series Patrician II or Patrician III? If I were to purchase just one of these which should I get?

Get Patrician 3 its actually the same as the second one just with the second's expansion.
If you read the first paragraph of the wiki on it, it explains the name differences between the english and german version.
[url=]http://en.wikipedia.org/wiki/Patrician_III[/url]

Ralackk is right, P3 is more than 2, but now the Patrician 1+2 pack is 50% off.

And includes the original Patrician, which is actually a splendid little game.

I recommend you to get Patrician 2 instead of Patrician 3. The difference is pretty big, despite similar 3D-graphics.

1. Better and realistically looking map in P2.
2. Ships are different: Crayer is faster and dangerous, Snaikka don't cost 1/5 of Crayer and have less potential to hold cargo as your wharfes get trained, Cog is slower but really useful due to the need to carry bushels of stapels. Therefore each ships have it's own role. In P3 I became patrician with only 3 snaikkas.
3. Food is profitable. In P3 fish, meat, bread available everywhere. In fact about 2 years should pass for grain to raise in price. In P2 food is scarce, meat price is high in the early game. Famines are possible. Therefore fish and wheat farms are good productions if you have capacity to transport bushels of course.
4. Events are actually happenning. Fires, famine, plague. Therefore building city services matters. In P3 I've seen only sieges. I think I never saw pirate attack on the city in P3. In P2 I've seen raids mentioned in the chronicle.
5. Regionmusic and seachart music plays.
6. Dirt roads are showing in the cities. In P3 dirt roads never appears, ven though they block building. When you pave roads it will just pave over the grass.
7. AI is better in P2. In P3 outsider cities never get visited. In P2 convoys comes even to Riga, Edinbourg and unload tons of cargo. Competition is huge in P2.
8. AI traders with heavy loaded ship may flip flags and attack other ships. Then you can see the same ships but under civilian flag again.
9. Different production capacity, different population balance. At the start of 1300 in P2: 24000 pop, P3: 55000 pop. You'll probably won't even find that much goods to fully load your ship in P2 at the start of the game.

Overall Patrician 2 is more interesting and harder game.

Is there a way to get die seachart music working?

I don't know and it seems like Patrician engine is moddable only with hex-editors, so no easy changes.

Just for clarification: in Patrician 2 you need to spend some time on "worldmap" to hear rare (3 to be exact 2-3 minutes each) tracks or odd chords of musical instruments from the folder Patrician 2/Musik/SeekarteMusic. Seems like on faster speeds (Normal vs Slowest) more music plays or perhaps it is tied to frequency of player's actions. There are also background noise from sea waves & seagulls from the folder Atmos, but it was present even in P3.

EDIT: I just tried again and no music plays. It's available in the folder Patrician3/Musik/SeekarteMusic/Seekarte01{,02,03}.mp3 but nothing to be heard in the game. Not even 1-2 chords, just awkward silence. I obviously prefer to play P2. Music there is so good you remember it for years.

Just replayed P3 and P2 and need to reclarify some points.
1) Patrician 3 is better in terms of user interface. Auto-trade remembers last price you have set for salling and separetely buying. It is possible to set the same command for every commodity with 1 click. Possible to set order for auto-repair. In P2 it's chore to set and adjust prices.
2) Pirates can loot ships without sinking and their konvois starts with more ships. In P2 only capture or sink. But pirates in P2 only used cogs, so they never were able to catch anyone. (Only possibility is to catch 100% loaded cog).
3) Ships "balanced" = equality strikes. They now consume equal amount of items to build. In P2 1 barrel of pitch, 1 ton of hemp, 3 cloth, 2 ironware, 7 timber; in P3 it will be 3 of everything. Communism desires that everyone must me employed, so wharfes started to use redundant amount of items. Monetary price is lowered. Can you imagine big sophisticated cog being cheaper than straight boat like kraier? Shnecks worth 1/3 of kraiers, nothing to said there. Speed is terrible: kraier in P2 worth at early technology levels (1,2) due to bigger carry capacity and load-per-sailor and stays efficient after 3&4 level of snaika (230, 250 barrels) thanks to the speed of 7. In P3 it have the same speed as shneck of 6. For the triple price and no benefits it will never worth the costs.
4) I was wrong about dirt roads appering. They never appear in both games.
5) They've added repair wharves everywhere because now you can't build ships in trading stations. Stations are cities where you can't build anything and are the most popular places, perhaps due to the fact they rarely grow and overproduce items thus having lower prices. They have had the most developed wharfes in P2 with the most developed weapons. In P2 you could build ships everywhere.
6) Added interactions with country lords at the gates... They seems to like only useless materials like hemp and bricks and timber... Gamey solution to overproducing. (Tip: nobody buys hemp and bricks). It's the free cities who would buy that goods from lords, not vice versa. The real question is why would mediterrian cities buy pitch in such quantities? And honey? Honey is used mostly for brewing alcoholic drink... Doubt people with access to wine would drink it.
7) Several shneck with auto-trading just iron goods rules in P3, don't bother doing anything else. In P2 I have 12+ ships and they still barely supply 3.5k city like Hamburg to grow, because you can have a situation when no one buys your iron goods. IG are the most profitable both by amount of trade and profit margin commodity in both games.
8) Cut weekly costs for a lot of productions, especially which seems unprofitable at first glance like grain. Yearly cost of production was ~136 for 1 ton of grain. Typical market price at the start was 110. Grain in P2 worth only in times of famine and should be set to sell at 175 for profit and 150 for 1-week satisfaction. Rathhouse notices might give even 212 for grain and orders a lot (20+ tons). Grain production mostly used for own consumption and to avoid famine in crucial cities. Cheaper cost and, perhaps, enlarged consumption led to things like "turkish building" and 2 million cities. Search for it, it's terrific. You don't need that density for P2.
9) Added city coffers to pay garnison and steal from, and ability to change city tax and rent for housing. Doubt they teach AI to use it, because it never changes anything, i.e. you can undercut AI competitor to have all the dwellers in your housing. In P2 city lord paid monthly garnison wage from his own pocket (44k per tier of walls).
10) Added useless council voting and hanse events which are hard to keep track of.
11) Most annoying addition: you can't skip naval battle when pressing fast-forward anymore. You must press Cancel. I don't care about battles, all my snaikas always flee in auto-battle anyway.
12) Cog is still as useless as before. For the 5 years I played the game I never ever had desire to build big ships. They are just useless. There are never that much daily/weekly amount of trade to justify added costs or repairs which take 1 month and 5000 sheckels. Late game easier to just make konvois from excessive ships, because even 1 snaikka upgraded to tier 3 bears 2 red circles of weapons... You need several per convoi to avoid being targeted. Add/remove non-upgraded trading ships for cargo capacity.

IMHO both games seems rather unfinished. Enemy ai stops being energetic after hitting 400k market cap. Rarely build production and sits at 1-3 ships, which he bought at auctions, slowly growing thanks to real estate rent. Never ever I've used public convoys option. Wait 5 days to trade with everyone else at the same time? No way. It also requires you to guess next port and be registered in guild, which costs a lot. Grey merchants indeed do pay depending on their load. Max I got is 470 for 150 barrels in snaika.
In one campaign you get ships with captain and loaded price-table and it's horrible. I wonder if AI uses the same charts? It's like counting flies and missing an elephant.