We've been to both areas multiple times, including Punta Cana the last two years.
I actually feel that Punta Cana is safer than Mexico. There are guards on the road on the way down to the Riviera Maya. No guards that I saw anywhere in Punta Cana. Given that, I'd have no qualms about either location.
In January it could be cold in the Cancun area, much less so in Punta Cana. We were in the Riviera Maya in January one year and the lows were in the 50's and one day it barely hit 70. In Punta Cana it goes down to perhaps the high 60's at worst at night, and mid 70's to low 80's during the day at the same time of year. So given that, I'd go to Punta Cana.
Both areas have tons of excellent all-inclusive resorts. Mexico is better for cultural activities off-resort - including Mayan ruins, eco-parks, ferry to Cozumel, cenote snorkeling, etc. Punta Cana has some things but much less so. You can take a boat to an island to snorkel. You can zipline or do a buggy drive adventure. But no major cities or cultural activities. In Punta Cana you can walk the beach for literally miles with no concern for safety. There are a lot of other vacationers from Europe, South America, and Canada especially. We like the cosmopolitan clientele and it's a change from the more US-centric Mexico clients.
Have fun, we really like Punta Cana for relaxation.