We did that sail in June or 2012 on our way to Panama. The preferred route was east around Cuba, through the Windward Passage, then straight-line to Cartagena. You have a better angle on the trade winds going east rather than going west through the Yucatan Channel. But going west does give you multiple stops along the way wher you can wait for good weather windows.
In our case, it was the beginning of hurricane season, and I didn't want to linger too long hopping down the Central American coast. We just made the non-stop run in 11 days, with 4 days of gale force winds and 20 foot seas crossing the Caribbean.
It was a miserable experience I would not want to repeat!
Our generator shorted out at 3 AM on the 3rd night of the storm, and the scare of a fire on-board in 20' seas, still 200 miles from shore was a horrible thing to go through! Fortunately, no fire broke out, but the smoke filled the cabin, and for about 10 minutes, I was going through our abandon ship routine in my mind, just in case. Realizing that the odds of getting the life raft deployed and us safely in it were slim to none is pretty scary!