I have the new xbox 360. There's no lag I've ever encountered and I have played people all over the world on the AVP forum. The original 360 basic didn't come with HDMI but that was soon fixed. All current models come with it and most older models do to. As Burple said the new 360 models come with wi-fi built in and the older models can be ethernet or use one of 2 adaptors that the 360 has on offer. You can also use a bridging router and connect that to your 360, that's what I did until I got my new one. Much cheaper than the 360 official one.
John is right, there is no reason to think that the same thing couldn't happen on the 360. Though I bet Microsoft have better security in place and have more financial backing to get it fixed a lot faster.
I'm easy either way as like Stoney I have both consoles. Just need to know which to get the game for.