In early 90's I was properly introduced to the world of DSOs, and that wonderful HP54600 (IIRC) was beyond anything I could ever dream - obviously unattainable for the common hobbyist. Fast forward a few years and I finally got my own oscilloscope, an analog Kenwood CS4025 (20MHz, 2 ch) at the incredible "bargain" of US$800.00 - not the HP, but my workhorse for 15 years. During this time I drooled over the low cost Tektronix TDS1000 series, but starting at about US$1000.00 it was still a bit steep for my hobbies - not to mention the analog was much more responsive.
In 2012, due to the eevVBlog's curse, I got the DS1102E at the unimaginable price of only US$400.00! I thought I was done with the analog, but after a while I still felt it was lacking the analog feel that my trained eyes were accostumed. However, the other advantages surpassed my old analog by a huge margin. It was not until Dave's review of the newly launched DS1054Z and its intensity grading that I felt a DSO would really make me feel at home again. I ended up getting a bigger guy (DS4014) at a bargain, although not in the same league as the other two, but this feature finally helped me put the analog at rest.
This whole story is only intended as an example of how things have to evolve technically and financially to overcome the hump between two discerning technologies - also, for hobbyists like me the financial plays a larger role. I think that in the 90's Tektronix did that with their low-cost monochrome DSOs and, in recent years, Rigol has done that for two generations with their DS1000 and DS1000Z series.
All in all, get an analog if you feel like playing with older tech, get the feel of observing the waveforms and require the extra bandwidth at a reasonable price. If you are working mostly with digital electronics, I would definitely recommend the DSO.
In the early 1990s,HP & Tektronix came to my then work (a TV Studio),to show us their "latest & greatest" DSOs.
I had seen a very early 1980s HP DSO which displayed a field rate PAL signal as a mess of random spikes like my untended back lawn,but I assumed the newer ones would be much better,so was as enthused as everybody else.
Unfortunately,field rate displays (around 4 div at 5ms/div)were still useless,due to aliasing.
The things had very little memory,so they dropped the sampling rate,until at that time/div setting,it would display simple waveforms only.
Even PAL line rate displays were very poor.
The Reps thought we were all "dinosaurs" because we weren't awestruck,& trotted out the script they were given,about it "being an equally valid way of looking at waveforms" etc,although that had nothing to do with the context of our misgivings.
They came back in successive years,until the DSOs "almost" made it,but they gave up after that.
We eventually got our first DSO---as a replacement for an analog Tek one which was a total "lemon".
It had driven Tektronix to despair,so they were glad to do the swap.
This DSO wasn't bad,------it saw field rate signals OK,but its sample rate at those settings interacted with the 4.433 MHz colour subcarrier,so it showed a non existent low frequency noise signal,which luckily could be disregarded.
When we bought a new Oscilloscope for the Transmitter site,however,it was a 200MHz analog Iwatsu.
We found the UIs on both Tek & HP 1990s instruments to be tiresome in the extreme,with often used functions needing to be accessed from menus.
The UIs on modern DSOs have converged towards that of analog 'scopes,with many functions available as individual controls on the front panel,making the learning curve between CRO & DSO & vice versa much less steep.
Modern DSOs of the DS1054z class & above can also handle complex signals at long time/div settings without aliasing problems.