The connotations are slightly different. Menschen goes into the direction of human beings, Leute is more like folks. In most cases they can be used interchangeably. However in this case Menschen sounds slightly better to my ears.
It doesn't matter about whom you're saying it
It does however matter who is saying it, in this case its you (ich mag) but if you wanted to say you like it should be du machst etc
Hope this was was helpful
Personally I prefer "ich mag Menschen" because I don't have to remember the "the" article. I also hear people use that phrase more often. I think it's the same differentiation between "I like people" and "I like the people" same as English. Not 100% certain though