as for me, there are 2 main differences.
one difference is the sound.
well… first, coming out: i am not a synth kind of musician. i am the drummer.
it was preambule, and here is the story: drum module.
for drum sounds, i mainly use old trusted Yamaha DTXPress III module from my e-drumset — either with drum triggers, like e-drums (full setup), or as a regular MIDI controlled sound module (portable setup).
as a session musician, i also occasionally use software only solution — MIDI controlled laptop running a sample based drum machine.
i experimented with a lot of sampled drumsets, but none of them even came close to the sound of hardware module just plugged in and turned on.
the recipe is the same for both setups — samples + reverb. both setups produce sound waves. but the sound is VERY different. what i can achieve with learning, exprimenting and processing in software, i have right out of the box in hardware.
i chose drum sounds as the example because my ears are well trained for drum sounds perception. much better than for distinguishing nuances in synth sounds. but anyway, i certainly hear the difference. a patch spied on a software synth virtually always sounds better when recreated on a hardware synth. sometimes the difference is subtle, as for my ears, sometimes i can't certainly describe it, but at least for subtractive synths (which are most popular type) it's always true. FM synthesis is different kind of beast, but i mainly use it for percussions and FX, so it's harder for me to tell about the difference, because it varies.
regarding the second difference.
i have a feeling that current kind of mainstream paradigm for computer-aided music production — laptop / DAW / plugins / that's all — is horribly wrong by design. the reason is very simple — it's a Single Point Of Failure kind of design. losing DAW operability means losing everything
. it's bad even for studio workflow, and absolutely inacceptable on stage. (but no one cares, because there are some advantages too, and they do matter.)
this was the main reason for me to migrate my rig to hardware. in most cases, losing one unit in hardware-based setup means losing only one unit. in a software world, no one can predict, will a crash of a single plugin crash the whole DAW or not
so, the bottom line is: software synths are excellent for education (if one is willing to learn something beyond downloading and switching presets), acceptable for production, but the hardware synths are just better.
(and note that i wrote „synths“, not just „software“. because if we speak, say, about sequencers, software ones are better than hardware.)