What's a hobbist? Is that a hobbit with a lisp?
I'm with crutschow -- the conveniences of the digital scopes greatly outweigh some of their disadvantages. My main complaint about the ones I've used is that they tend to be harder to trigger than the good analog scopes I've used. But they're getting better.
The features I use and like the most are:
Being able to press a button and have the waveform saved to a thumb drive. This completely beats out the old method of finding the Polaroid camera, film, and hooking things up, then coating those stinking pictures. You young punks haven't lived until you have to get 50 or 100 waveforms taken, then pasted into your lab notebook.
Yeah, it really sucked!
I look at transient stuff a lot and I've never used an analog storage scope I was overly impressed with. The digital scopes really shine here.
I use the FFT and math stuff substantially less than I thought I would (I can look at a signal and have a pretty good idea what its FFT looks like and about the only thing I use the math for is the occasional plotting of real-time power waveforms).
A feature I use a lot is the digital filter on the input channel. It is very handy to be able to e.g. band-limit a signal with a few button presses. This is much cooler than routing your signal through one of those Krohn-Hite filter boxes.
I also use the measurement functions a lot -- I use RMS voltage, peak-to-peak voltage, and frequency the most.
As far as I know, all the inexpensive digital scopes are made in the far east. I've used one or two that I weren't terribly impressed with (and one failed while I was using it). I have a B&K 2534A on my bench currently as a loaner and it's OK for most of the stuff I do. When that scope goes home to momma, I'll go back to my HP 4 channel 100 MHz digital scope, which is still a pretty good scope even though it's about 20 years old.