We have been to tulum several times and chichen itza once. We visited while staying at all inclusive nearby. Keep in mind the travel time to both from the ship. It involves ferries and varying lengths of bus rides.
Of the two, I would recommend chichen itza hands down. It was one of the best places we have ever visited. The history there is amazing. We were able to spend several hours there and experience everything with a guided tour. We were even allowed to climb up the pyramid!
The last time we went to tulum, it had turned so commercial. They had set up vendors at the ruin site, not at all like the first time we visited. The beach at tulum is one of the prettiest we have ever seen though.
Just wanted to share a different memory of the same site. We went to Tulim with
DCL. It was a 30 minute Ferry ride and 45 minutes on the bus, but that still left us with over 4 hours at the ruins site. The tour started on the bus with the tour guide telling us about Mayan culture. When we got there, the guided tour lasted about an hour, which was a perfect amount of time for information and seeing the sights, and that left over three hours to explore the ruins on your own, go to the beach (yes, it is a BEAUTIFUL beach), or shop. Personally, I didn't find the site to be nearly as pushy or commercial as some other places we went on the same cruise. The vendors were all a fair piece from the actual ruins sites and the beach, and they could be completely avoided if you chose, unlike a lot of places. Also, the tour guide had a wireless headset and we all had headphones, so we could hear him clearly without having to fight to stand next to him. This made it a lot easier to see and hear everything. I wish more tour groups did this. One criticism I had was that the included "lunch" was a ham sandwich from a cooler. But they did give each person two bottles of cold water, which were very much appreciated. It was a HOT day.
To the OP, I'd say it depends on your attitude and what you want from the trip. If you want a quick trip, do the one on the island. The ruins are lessor, but you'll have more time left for other things. If you are super excited to see the "best" ruins, go to Chichen Itza. (I didn't know they still let you climb it.) It is an even longer bus ride after the Ferry, but surely the biggest ruins site. For us, Tulim was a good middle compromise. I was worried at first that Tulim wouldn't be "big" enough, but for us, it was. It ranged all over and was quite beautiful.
Let us know how it works out for you!