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

You cannot be a serious EE if you have to have both digital / analog scopes.

More rubbish from dear Henry.

There are expensive digital scopes with digital phosphors but they don't work in all situations.
The main use of an analogue scope is looking at a modulated signal on a HF carrier, try that on even the best digital scoopes.