Which is the best Xenoblade game? Always wanted to play this on an emulator, but never got the chance.
It seems to me that the answer to this question depends very much on the player. I will lay down my perspective and explain, maybe that helps.
XC1 is for me personally one of the best games of all times, so I am definitely happy about the remaster. But it has some flaws, maybe the remaster will fix some. What stands out in XC1 is in my opinion the music. I seldomly heard that great and memorable music, that emotionally connected very well with the plot. The second area that makes this game great for me are the characters. HoangNhatAnh might be right that character arcs are better in XC2, but the characters in XC1 were so lovable. I connected very well emotionally with them. Shulk, Fiora, Reyn were such a great team, I loved being with them. And Sharla and Melia were great additions. I loved also heropon Riki, much better Nopon-character than Tora (XC2). The third greatness are the environments. The feeling of freedom and how well it all was placed onto the body of the titans, it gave a feeling of a great area. And how different it all looked at day and night. The plot was good too. The downsides are visuals (which look improved in the remaster) and clunky combat. Don't get me wrong, the combat is strategic and deep, but it can be difficult to get it done right.
XCX was not a bad game, but some things spoiled it for me. After XC1 had so great music, I was disappointed in the music. It mainly was one track that was bad, but sadly that was the music of the hub, a sort of base/city. That by the way was another downside for me. XC1 had no hub or base, you explored the world, always pushing on. In XCX you have the base and mount missions, but get back to base. It felt less like an advanture that way, more like a military expedition. I also have barely any connection to the characters. I think there were way to many of them and all their story arcs were separate. The plot was also split in chapters, which disconnected me a bit from the story. I think this was to better fit in the online, but I give a crap on online. On the upside I think this game has the best visuals of the three. I like the comic style of XC2, but frankly some areas and monsters of XCX look absolutely stunning. I am usually a defender of unrealistic artstyles, but the absolutely beatiful and strange world of Mira feels more otherworldly because of the more realistic artstyle. This seems counterintuitive, but with a more comic style I always feel the artstyle represents something else. If you see these alien plants in all their strangeness and the realistic artstyle, this seems more impressive. The mechs were OK, I felt they didn't add much to the fighting. But they indeed add much to exploring. The mechs made traversal so much easier and really helped to reach some areas. Ah yes, the game has mechs. If that is your thing. XCX has a real open world and offers a lot of additions in the sort of exploring.
XC2 didn't get me so much in the story, so I havent played it through yet. As I said I like the comic visuals, I only felt the more realistic style helped me to impress me more with the sort of bizarre creatures and landscapes. But also XC2 looks beatifully. Both XCX and XC2 clearly outshine XC visually (no surprise as the first one wasn't even HD). The music is good, although personally I still prefer the one from the first game, but that may well be personal bias. XC2 introduces again a more strict plot and better characters than XCX. So it feels closer in these areas to the first game, although I personally preferred the first one. The fighting in XC2 is much more streamlined and feels more organic. The arts are mapped to face buttons now, so they are easy accessible. The idea of the drivers and blades feels a bit strange at first, but it allows with a relatively small cast of characters (that you can better emotionally connect to and that better fit into the plot) to have a wide variety of fighting styles, as each blade offers different abilities. If you unlock a lot of them this gives you great possibilities for configuration.
Well, I hope my impressions help you a bit to get an impression of the up- and downsides of the three games. Overall I can recommend all three.