I use both plugins and pedals, often interchangeably, and enjoy doing so. One thing I like about working with software is being less in the moment, being able to do some work, walk away, and start where you left off, go back and change what you've done. It's a different process from playing, much more like score writing or painting. Strangely, I find I approach software as a slower process than working with hardware, which is a very in the moment kind of thing.
There are still a lot of things you can do in software that are difficult or at least really pricey to do well with standalone hardware: granular effects, FFT-based spectral processing, complex multi-tap delays. Even fully stereo signal chains can be difficult to achieve with pedals, since so many are mono devices. That at least has gotten better in recent years with the advent of Eventide stompboxes, strymon, jomox, oto biscuit, etc.
To answer one of the initial questions, one thing that software has a tough time capturing that is inherent to analogue devices is irregularity. Individual components in, for example, a fuzz pedal have a lot of influence on the end result and are context sensitive (change with input gain, room temperature, power fluctuations), and so you are working with something unique, albeit at times rather subtly so. 112db's retro sampler Morgana is I think the only software I've seen that tries to model irregularity with a function that allows you to calculate filter coefficients unique to your system. I wish more softwre developers would explore that technique. The upside of the absence of irregularity is reliability, which software has in spades.
Along similar lines as what Taylor said, standalone hardware devices offer a certain immediacy that software lacks, just by occupying a physical place in the world, and offer natural limitations. They also require a lot of dicking around with power supplies, storage and cabling, the like of which can be enough to drive you to software.
