The XBox was (relatively) easy to develop for because of how closely it matched a PC in terms of hardware and development tools; the CPU was an Pentium 3/Celeron hybrid running at 733MHz, its GPU was based on the Geforce 3, and most interaction with the graphics hardware was handled with a modified version of DirectX 8. This closeness to the PC is why the XBox received so many (often console 'exclusive') PC ports, why so many western third party developers favoured the XBox, and (potentially) why the XBox performed as well as it did.
After how many developers struggled with the N64, Nintendo focused on producing a system which was much more straight forward, had few bottlenecks and provided excellent real world performance. The Gekko processor was designed by IBM using their G3 core (the same basic core at the heart of the XBox 360, PS3 and Wii) with an extended instruction set; the Flipper GPU was designed by a small hardware company founded by former silicon graphics engineers who were devloping flight simulators named ArtX. Overall the few third party developers who really focused on the Gamecube (Factor 5, Capcom) achieved some amazing things, but most third parties did rushed ports of PS2 games and never took advantage of the Gamecube's capabilities.
The PS2 was a disaster in terms of ease of development and many initial PS2 games looked worse than Dreamcast games; third parties started to achieve amazing things on the PS2 mainly because its sales ensured that it would be the target platform for (pretty much) every game, the extra money needed to optimize code (or licence highly optimized middleware) was justified under the assumption that improved graphics would increase sales of the game.
As a guess, the PS3 is facing so many delays this generation because managing a project as large as PS3 games are becomming is not a simple task. In most software development (or any engineering project) a team of over 10 or 15 people is seen as very large and you need a highly experienced person in charge; many of these PS3 games now have teams in excess of 100 people and timelines of 3 years, like all projects unmanaged risk could delay these games by 50% to 100% of the initial timeline.
