Welcome to FT !
As a fellow FTer in the LAX area I figured some things about the carriers serving our beautiful port to the west: They all suck... thanks to the great LAX gateway management. Now it's the question which one doesnt suck as much as the other ones.
AA: They have the direct flights to MIA, however nothing direct to germany and the overseas trips there (I do 2 a month) cause you to get up at least at 6 am to get to the airport for your connecting flight. But the flight arrives later in FRA than the direct *A flight that leaves LAX in the afternoon. No Go!
Yes, you get free AA upgrades as EXP, but look at their cabins/planes on domestic routes. You find more ductape than a stage worker uses in a month. Hardly can you call that First Class anymore and to pay for it in whatever currency is not even worth the thought. The status challenge on AA costs money while others offer it for free. After 100K miles you get Executive Platinum status and unlimited free upgrades (I commented above on their cabin comfort, better than AA coach though) as well as 8 systemwide Upgrades into an acceptable Business Class to germany (as long as you fly via DFW, the ORD 767 is dreadful and the staff there as well). The Club in LAX is pretty nice, good staffed and clean. AA has an elite check-in area but if you have to check bags it's still horrible to say the least.
DL/NW: They merge but you could get a free status match right now to Northwest Platinum Elite and I would say 90% of your upgrades will clear. The times I think of them as Northworst are over for a while and their premium cabins and planes are fine. The clubs have free booze if thats important for you. Pricing is also VERY competetive out of LAX ! I just start trying them a bit more so I cant comment on this particular alliance that much. But they offer many routes out of here !
UA: I switched from AA to UA to figure if the grass is greener on this side. Last year UA was horrible, in the past few months I really feel an improvement with them. Anyways, lets see the hard facts: The "Business Only" flight to JFK that you are talking about is called P.S. ! It is absolutely NOT Business only. If you sit in coach you have the worst Economy Plus seat-pitch of the whole fleet. In Business the seats are nice but upgrades hard to get if you upgrade with E500's (200$ 4 upgrades, you need 5 for JFK). IF you get the upgrade you will be surprised by a nice

little cheese platter and maybe ice cream. Thats it, enjoy ! United might offer you a challenge to fly 15K miles on UA within 90 days to get Premier Executive. But I'm not sure because US Chairmans is a *A Programm. You could cross match through NW though ! Your advantage especially with your trips to germany is there are plenty non-stops on *A (3 LH flights and maybe the UA flight will return next year). When you get Top Elite 1K you will recieve 6 systemwide Upgrades, 2 CR1 each quarter for every 10K you fly on UA plus 4 E500s for every 10K, UA's F cabins are ok IMHO. No unlimited free upgrades like AA or NW though ! UA is my current choice together with LH. In case of Irregular operations you will again have plenty of options to get rebooked on while the other carriers are somewhat limited. US has a Red Carpet Club which is ok but not famous for it's service level. I hate the RCC's anyways and just use them because I can enter for free with LH*G. UA's elite check in area is in Terminal 6. It works well I have to say as long as you dont need a rebooking in peak times.
Hope that helps to give you a little impression !
Cheers,
Seb.