There are a number of little differences between the two, such as changing when White Base
goes to Texas colony and some similar timing changes elsehwere, but there aren't any major plot differences that I can think of that would radically alter ones view of the story. As for which version to show, it depends on your friend. If he has the time and is willing to sit through the 42 episodes of the original series, then go with that. If he doesn't, or simply wants to get through it faster, and is still pretty new to Gundam, the movies are probably the best option. You really can't go wrong with either version, and it comes down to what your friend is up for.
Plus, the movies are usually considered the canon version of the two.
As we just said last week
, the movies and TV series have exactly the same standing and one isn't any more canon or official or whatever than the other.