I think the main difference is, some country can put the squeeze on a place like Panama, like another poster said. I can imagine the Panama Canal in TTL becoming a Central American version of Hon Kong, where the British sort of muscled in and said, "We're building this here, and you can't stop us, but co=operate and it might be worth your while."
I don't know if any other country had the means plus the will to build the canal then, however; maybe France, i guess. And, without the canal, I don't know if anyone would want anything more than a few islands in the Caribbean.
Hmm, thinking about it, that might be the biggest change. An 1880s/1890s battle for Panama, which could lead to a variety of interesting things.