My GI also prefers Remicade, Humira, then Cimzia. Mainly due to research, time, and having patients on it for longer periods of time. There is more known about drugs around longer periods of time.
I have taken them in that order - and that was even before I came under his care. I am now on Cimzia. They all have similar possible reactions, similar possible side effects, similar costs. My insurance company is not as keen on approving Cimzia due to it being new but approved it for a few months until the GI can "prove" it's working better than Humira.
I'd personally move to Humira and hold off on Cimzia. It's been around awhile longer, you'll be able to talk to more people who have been on it or still on it, and more is known about longer lasting issues. Save the newest stuff for when you're at that point.
I agree that most docs want to do them in the order of Remi, Humira and then Cimzia. I did them a little out of order since I did a clinical trial for Cimzia before it was on the market (before trying Humira). I am now back on Cimzia since the Humira was not helping enough with my arthritis.
Both Humira and Cimzia have the same copay for me (if I were paying a copay, but both have programs where you can get it free for about a year), but Cimzia is probably more expensive to your insurance company, since it is newer, so you may want to look into that. It was great to get Cimzia for free for a year on the clinical trial, then get Humira free for a year through their program and then switch to Cimzia and I'm supposed to get it free for a year. Yea!
I had more trouble getting Humira approved through insurance than Cimzia. It took over a month with several rejections and letters from the dr. to get Humira approved. My Cimzia was shipped a week after I got the prescription from the dr. (and I even had to mail it in). I was very surprised that insurance had no problem with me getting it.
Humira hurts a lot more, but I did my Cimzia injections last night and did not allow them to sit out for the recommended 30 minutes first and they stung a lot worse than normal. Both of them have kept my Crohn's in remission. Cimzia seems to be helping more with the arthritis at this point, as it seemed the Humira stopped working as much after about a year. So, it's completely up to you, but I think Humira and Cimzia are both very similar.