I'm 99% sure that the PS2 wasn't online ready at launch. I bought one just a few months after it was released and don't remember the option of any online features. I think it was the slim model that came later that allowed for online functionality.
Yes, Microsoft did a great job bringing online gaming to the forefront, but that was always their thing. They are a computer company. They deal with online features all the time. They were ahead in that department to begin with. Sony has done just as much, if not more in other areas. Microsoft only came into the game console world because they felt threatened by Sony and felt that the Playstation was going to take over PC's.
In the end though, it doesn't really matter since both companies have had their share of ups and downs. To me though, Sony is the company that keeps raising the bar technologically and at the same time, delivers a product that not only kicks butt, but is built to last. It's not just about the RROD with the Xbox. Microsoft has routinely made products that either crash or have glitches and their monopoly over their industry has turned me off of their products.
Edit: I guess there was a network adapter that you could buy for the PS2 before the slim model.http://en.wikipedia.org/wiki/Ps2 So basically, Microsoft got the idea and took it to the next level.