Mad Dave Jones... yeah, we've seen him.
I doubt he said you need both types of oscilloscope. I've never seen him using anything analog.
Is this the video you mean? EEVblog #86 - Buy a real Analog Oscilloscope PLEASE! - YouTube
What he's saying there is that if you don't have any money you should buy a second-hand analog scope instead of one of those pocket DSO things off eBay.
The eBay 'scope he tried was this one: EEVblog #359 - QDSO Pocket Oscilloscope Review - YouTube
That one is a pile of garbage, to say the least. There's a different one called a "DSO Quad" which is orders of magnitude better but doesn't cost much more than that one.
OTOH he has a point. "Real" 'scopes have much better controls and internal circuitry. The DSO quad works well enough but the user interface is horrible and the bandwidth is probably below 10MHz despite what the sellers say.
If you're serious about electronics it's worth waiting a bit longer and saving up to get a proper digital scope.