Hi!
I've been on both as well as several others (Enbrel, Humira, Methotrexate.)
After being on Remicade for some time, I developed a melanoma on my nose.
Note; the overall effects were not great ; but none have been that successful for me.
As I am overweight, and the Remicade dose is based on weight, I was receiving quite a high dose.

An oncology team and the rheumatologists I was working with said that I could no longer be on the biologics for my RA. As a result, I am now on Remicade as it seems to help somewhat - not a complete "fix" but there are some benefits: somewhat more energy, a little less stiffness.
There have been no significant side effects from the Rituxan - a little weakness after the infusion.
I am also on azathioprine for RA.
It's been my experience that the meds seem to work for maybe 2-4 years, then seem to slow down on their effectiveness.
Best of luck on your journey!