Should a serious hobbiest/EE own both a digital and and an analog oscilloscope?

A couple of years back I managed to snag a nice Fluke Combiscope; it's an old dual-channel DSO with both analog and digital modes (you can set the traces so that one is analog, one digital, or both analog or both digital). You'll only find such a scope, I believe, in those with real CRTs. They likely don't make them any longer.

I'd say ultimately the answer would depend on what you plan to do in electronics. For most hobbyist needs, a cheap 50 or 100 MHz Rigol or similar DSO would be all that would be necessary. The only time you might find yourself needing an analog scope would be for things where you need to catch the "transients" that the sampler might miss (as has been pointed out by GM above).

If you know what you are doing to test out a scope, and can do it in person, buying a used analog scope can be worth it. I picked up a Tek 2213 on craigslist this way (it had even been factory calibrated). The only "repair" I had to do to it was replace the implosion shield (the old one had gotten fogged up - I knew this when I bought it - the replacement came from this Tek parts site in Czechoslovakia). I paid $250.00 for it (the Fluke I only paid $200.00).

One thing I did find out real quick was that even on the used market, once you advance beyond 2 channels or 100 MHz of bandwidth, the prices skyrocket like nobody's business (though I did once see a nice Tek 4 channel scope at a local ham fest for about $250.00 - so it is possible to score them occasionally).