I am Catholic, my wife Russian Orthodox.
Didn’t read all the answers above so don’t know if these came up:
similarities:
-Mary is regarded as very important in both religions, even though Orthodox Christians say that Catholics at some point decided that she was born with no sin thanks to the mercy of God. I agree with them that this would make the devotion to her useless as she would have no merit in her purity and devotion to God.
-Spiritual imagery is very important in both, in Catholic churches you will usually see many statues of Christ, Mary and saints as well as paintings while Orthodox Christians prefer icons.
-the practice of monasticism.
-certain parts of the mass: reciting of the ‘Our Father’, the reading of the scriptures, communion, priest sermon.
I am catholic and got married recently with my Russian Orthodox wife in her Orthodox church. We were a bit worried that the priest may challenge the fact that I am Catholic but actually he seemed relieved that I wasn’t protestant or of a non-christian religion as he finds Catholicism very close to Orthodoxy.
However, he also went on making his point on why our calendar is wrong… and the orthodox bishop whom we also met said that they too are ‘Catholics’, meaning that they belong to the ‘universal church’. So he clarified that it is not just us being part of the universal church, but them also. He explained that they are ‘Catholic Orthodox’. This was new to me.
Some differences that may interest you:
-Russian Orthodox masses are usually much longer than Catholic ones. On a Sunday at my wife’s church the mass will last approx. 3 hours. People stand and churches usually don’t have benches. I did however hear that Greek Orthodox churches also do have benches (but not sure about this).
-Orthodox Christians don’t pray the rosary. However they may pray the ‘Jesus prayer’ on a soft chain of beads (it is soft so it doesn’t make noise and doesn’t distract the prayer). I noticed however that Orthodox Christians don’t give this type of prayer as much value as we do for the rosary. It appears to me that the mass prayers are more central.
My wife and me feel very inspired in praying Jesus and dedicating our lives to Him despite the different Christian denominations. We start having a bit of a conflict when she starts telling me that theirs is the true Christian religion that didn’t change but maintained the original Christian tradition. While I appreciate the richness that comes with the fact that old traditions have been maintained in their belief, there are parts of the Catholic faith that I can’t do without, like the rosary.
To me, our situation feels often a bit like if we were two different professional and first league football teams. We may have different shirts on, but we play the same sport at the same professional level

Sometimes one has the better, sometimes the other…