I've had a an xtracycle for the past 5 years and upgraded to a Big Dummy this past summer. I used a Burley trailer when my kids were smaller and then moved my daughter up the back of the Xtracycle when she was about 4. My son stayed in the trailer until he hit 4. Now, they both ride on the back and I have passed my trailer on to my sister-in-law.
I really liked using the trailer for as long as I could. The kids were always protected from rain or sun and could fall asleep without worry. They had their snacks, books, and toys with them and always seemed content. When they got too big for it I was happy and sad. I was happy becuase the trailer really slows you down in the wind and sad because I had to worry about my son staying awake while we road- there was no pea-pod option at the time for him. I have a couple of camping/kayak seats strapped onto my deck and the kids sit on them without issue.
Last year i picked up a tandem with a child's stoker kit off of C.L. and thought my daughter and I could ride that while my son rode on the tag-a-long attached to the back of the tandem. The set-up works great when it's just my daughter and I, but it sucks when my son is added into the mix- he's a bit of a slacker. I find that I can move faster with both of them on the back of the Big Dummy than using the tandem and tag-along set-up. If it's just my daughter then the tandem is faster, but she actually likes to pedal. She's also older (8) than my son (6) so I imagine he'll be a better biker as he gets older.
I'm not car free, but living in Madison I find that I can pretty much park my car all summer long when I'm off with the kids. During the winter i need a car to haul them around, but have a winter bike for myself that works out pretty well- as long as I remember to put on the studded tires.
I would say to get both if you can. I was luck that my neighbor has a single seat Burley and I had a double. When she had another kid we traded trailers for a year or so while i got to move my daughter up to the back of the Xtracycle. Pulling a dingle trailer was much easier than a double. When both of our kids got to big for the trailers we switched back. i was able to pass mine on to a family member and she was able to get some of her money back from C.L. If you're really going car free I think it's worth it to have both.

Jon