You might also wish to consider LH's Miles & More if most of your travel is going to be in J. You'll earn 200% of flown mileage, although intra-European segments will earn a fixed 2,000 irrespective of distance flown. F earns 300%. LH changed their program earlier this year, making upgrade awards more expensive, and reducing earning in the lower fare classes, so it's not as attractive an option as it once used to be.

I switched from UA to LH at the beginning of the year due to the more generous mileage multiplier for J and F, so as to attain status more quickly. When flying on LH, OS or LO you'll also get a 25% bonus if you're FTL (*S) or Senator (*G). Status is reached after 35,000 and 100,000 miles earned, and it's valid for two years. Now that I have Senator, I'm considering whether to go for a different *G next year; UA is still attractive with the eilte bonuses, but they may not be around long-term.

I haven't been around the LH program long enough to comment on upgrades, but you do get better lounge access in the US with a Senator card than the UA equivalent (much like BA Gold is better than AA EXP).

As for comping status, you might want to try UA if you have AA EXP, bmi if you're BA Gold or just generally LH. I have no personal experience of this though.