I played three of them because until I imported Extreme VS, they were the only modern gundam game I could play.
The first one was pretty shit. Not a lot of characters or suits, weak plot, pretty meh.
I skipped the second and played the third. Ton of fun MS to choose from, not terrible story mode with some fun interactions (like Full Frontal and Treize having a gentlemen-off basically) I loved the cell shaded look. It had a decent customization system.
I have mixed feelings about Shin Musou. It added a ton of new MS, but they were basically all from Seed. Seriously, can someone explain Japan's hard-on for Seed? Because we got nearly every MS from both series while only adding the Banshee, Geara Zulus, Delta Plus, and some DLC suits like Crossbone. It has an interesting customization system that requires you to choose whether you want to upgrade special moves or layer upgrade plans to boost stats. Much more interesting than upgrading some stats in 3.Shin also made some gameplay tweeks that I think damaged some suits…I don't know why but the Burning feels very nerfed. It was a monster in the old game and here it feels like it doesn't do enough crowd control damage.
Shin Musou does have my favorite story mode by far, you get a mish mash of different characters and factions fighting against each other based on what scenario you are running, and it does a fun job playing characters off of each other unlike the more generic 1st and 3rd story mode involving the Musha/Knight Gundam teleporting everyone to a battlefield for reasons.