Dan's answers are pretty much on point. As a person who prefers simple complications, I have spent a considerable amount of time looking at this comparison (I'd also include Lange's Saxonia in the mix because it is in the same league in my opinion). Of course you are at the Hour Lounge, so my answers are a bit biased ;). But to answer your questions (Alex G, I am sorry if I am using price ranges here, but its difficult to help without acknowledging Alexe's restriction, so feel free to edit as necessary):
1. Yes, in some cases I find the finish better (very minute at this level, but its the little details that stand out). For instance in the Patrimony Traditionelle line there are small curlings at the bottom of the case that are just stunning. As for the Contemporaine, well its an icon and the case is light, thin, and perfect for a dress watch. More so, I don't like the fact the Patek rhodium-plates their gold watches. Yes, it gives them a shine, but over time it is not optimal in my view. I much prefer Vacheron's solution of using more Palladium (came about around 2007), which gives the shine a warmer feel and doesn't look weird years on where you tend to find unevenness in the shine with the Rhodium-plated watches . As Dan mentioned, the depreciation is market-controlled and Patek is a much bigger player in terms of production (just over double) and market spread (they were fast on the name spread and marketing to establish themselves as what some see as 'the' premier mainstreaml watch brand). However, in recent years, Vacheron has been doing quite well (and stronger). So we shall see.
2. VC Patrimony for the aesthetics, finishes, and overall look. The Calatravas have tended to strike me as a bit boring (and the opaline dial that sometimes comes in the Calatrava range, which is now referred to as silvery-grey, is just not to my taste). Again, here I would not discount a Lange Saxonia, since it is just as well made (and with the low production numbers, less likely to run into someone wearing the same). Of course, I am not you and our tastes may significantly differ.
3. In your price-range (I am assuming USD) your realistic options if you are looking for a new piece are (don't forget the relevant taxes to be added):
Patek: honestly you are looking at 20-25k even with manual references such as 5116, 5119, and 5196. Haven't heard anything on the pricing of the new ref. 5123, though, but doubt that it will be significantly lower.
Vacheron: here it is more the 18-20k when looking at the manual winding references 81180 (Contemporaine) and 82172 (Traditionelle)
Lange: Saxonia manual winding or Saxonia thin (at 40mm but what a beauty) should both be under 20k as well.
In the secondary market, you will have better luck. A cursory look on some websites can give you an idea, but the preference is to always check with an AD, especially since there are too many fakes out there. That said, on the secondary market, as you noted, Patek are higher priced. Considering the budget, I'd personally focus on finding either a Contemporaine 81180, a Traditionelle 82172 (lmore difficult since its newer), or a Lange Saxonia manual winding or automatik.These three may be found in the 10k -12k range in very good condition (or better if you are lucky). In any case, those would be (and in the past have been) my choices - again, some bias here ;). That said, if you look at older models, there are deals to be had especially if you look at the ones on auction where some Vacheron beauties are being acquired for fantastic deals. When looking at older Vacheron models, I'd suggest checking in with us here before pulling the trigger so that you can be confident that your choice is authentic since the people here are as knowledgeable as they get (even auction houses sometimes get it wrong... I'm looking at one with the letter 'A').
4. Again, as Dan mentioned, is your comparison between (a) a Patrimony Chrono and a Historiques Chrono or is it (b) between a Patrimony (Traditionelle/Contemporaine) and a Historiques Chrono? In the first instance, I'd say go Historiques Chrono since they are based on a similar ebauche and the Historiques Chrono can be had for below 20k on the secondary market. Plus its got that beautiful vintage feel, and if you find one with a Salmon dial, well you will be the envy of many of us here ;). But if your comparison is Patrimony Traditionelle/Contemporaine or a Historiques Chrono, it is a veryy different comparison where you have to ask yourself whether you are comfortable pulling off a Chrono as a dress watch. To me a dress watch is a 2 or 3 hand manual winding, understated, and discreet watch so I'd avoid the chrono for that purpose -don't get me wrong, I love chronos, but very rarely wear them as a dress watch.
Ultimately, it is a tough choice and I would recommend looking at the options over and over again - its a significant purchase that needs to be weighed properly and well-thought through. I think you are asking some of the right questions, and I'd recommend you ask them on the patek forums as well (to balance out the bias ;)). But remember that the watch as investment question is not ideal since preferences change, and who knows, ten years from now the market dynamics might be significantly different... At the end of the day, the way I see it is that you are not only buying a timepiece, but also joining a community and in either case, it is not a bad place to be ;) - but my preference is clearly VC.
Good luck, and do let us know how things are coming along. Hopefully you will share with us a pic of your final decision -whatever it may be!