Why does a portafilter machine take so long to warm up and a modern machine doesn't?

By portafilter I assume you mean the standard large coffeeshop espresso machine.

The Nespresso is only heating enough water for a single shot, which can be done pretty quickly. I'm pretty sure commercial machines take a long time for that first shot because they're preheating the large reservoir so it's possible to fully heat and pull shot after shot in fairly quick succession once you get going.

So the lag is because the bigger machine is heating a bunch more water--even if it doesn't superheat any more per shot than the Nespresso.

Somebody correct me if I have this all wrong, but that's what I was led to understand.

It'll depend on how much stuff you need to warm up to maintain acceptable thermal stability. In a typical machine, you will have a brass boiler, attached to huge chunk of metal that the portafilter fits into,the grouphead.

http://en.wikipedia.org/wiki/Grouphead

The water in the boiler will probably heat up pretty quickly. However your grouphead and basket will still be cold. If you pull a shot now, you'll lose heat to the surrounding mass. This is no good when you are trying to maintain a particular temperature.

15 minutes is probably too short to wait though. I am waiting at least 30 minutes on my domestic machine with an E61 grouphead.

If you look at a Nespresso machine, well there is not much machine. The ones I have seen are kinda plastic-y as well. So not only are the internal water paths very compact, but they wrap the entire thing in an insulator. Probably pretty efficient.