Xbox – play GTA IV’s multiplayer with a different disc (DLC / original game) than the friend

Yes, it is different.

Episodes from Liberty City only contains the expansions Ballad of Gay Tony + Lost & Damned. It does not contain the storyline from the original GTA IV. I would assume the size is so large because it includes most everything from the original game. The Xbox 360 expansions both weigh in at 2GB+ by themselves. The expansions make use of most of the entire city and have all the same vehicles, guns plus more.

Running Hangman's NOOSE over and over again with a solid group of people who know how the situation plays out exactly and can communicate is a great way to earn money. You can run NOOSE with random players, but if you aren't winning every time and doing so in just a few minuets the rate at which you earn money isn't as high as it could be. The OP might consider this a "boosting" answer since the money gained is higher when working with a group of well coordinated players, if so just disregard it.

I'd still say that Hangman's NOOSE is the best way though, because when it goes well you win rather quickly, and when things go bad, your group is killed rather quickly. The other forms of multiplayer (DM/TDM/Racing/Turf Wars/ect) can take much longer and don't return nearly as much money.

Just be warned if you are looking to get the Wanted achievement/trophy. The grind to it ($5,000,000 gained in multiplayer) will take forever no matter which method you end up using.