I wouldn't say that either of the two Chomskyan distinctions you describe has supplanted the other; they're both still standardly assumed.
On the competence/performance distinction: imagine, for example, that I begin a sentence with "This is the…" and then I inhale a fly, so I stop talking. And imagine further that I never go back to finish that sentence, having been too traumatized by inhaling a fly.
We think that the way you talk is the product of many factors, including your memory, the condition of your tongue and teeth (or your hands, if you're signing), how tired you are, how likely you are to inhale a fly…and also, somewhere in all that, the parts of your brain that are constructing sentences for you to produce. 'Performance' refers to the result of all of these factors. 'Competence' is just the part of you that is responsible for producing linguistic utterances, minus all the possible factors that might interfere. Your competence might never produce sentences like 'This is the' (maybe it was trying to create the sentence 'this is the first day of spring', or something like that), but the sentences produced by competence can be altered by the various other factors that make up performance.
I-language is not unlike competence; it refers to the properties of your internal 'grammar', the part of you that's responsible for producing utterances. And you have an I-language which probably resembles that of, say, your siblings, if you have any; you and your siblings would have more or less the same vocabularies and rules of grammar in your native languages (though these might very well not be completely identical). And if we compared your i-language to those of all the people who grew up near you, again, we might find a lot of similarity, though still with some differences. This has to do with how human beings grow up and acquire language; we tend to end up with i-languages that are similar to those of the people around us.
A Chomskyan position on the nature of language is that in the final analysis, i-languages are all there are; there are people, who have individual grammars that determine how they speak. And because of how human beings acquire language, we tend to end up living in large groups of people with pretty similar i-languages. If we wanted to, we could call these groups of i-languages something else, like 'languages' (or Chomsky suggests 'e-languages', for 'external languages'). But it's worth bearing in mind that these 'e-languages' are fictional; they're just a handy way to refer to these large groups of roughly similar i-languages.
This way of talking is meant to, for example, allow us to avoid trying to answer questions like 'how do we know whether two people really speak (dialects of) the same language, or two different languages?' The answer to that one is 'There are no such things as 'languages' in the sense that you mean; what ... (more)