The next step up in DMM prices seems to be around 400 euros and I have no idea if those are any good.
Why the heck is a decent DMM with far fewer knobs, connectors, a simpler display and much less processor power more expensive than a perfectly useable scope?
Because the complexity in a cheap scope is in the software and user interface, while the complexity in a bench DMM is in the bits of hardware deeper in the box.
Most bench DMMs focus on accuracy and precision. Maintaining high accuracy becomes exponentially harder as you increase precision. Noise becomes a huge issue to deal with. And you want all this while having decent input protection.
Oscilloscopes are not designed for high accuracy or precision, because measuring is not their job. Their hardware complexity is from needing to support high speeds.
Consider this: a cheap oscilloscope (as well as most expensive ones) usually has an 8-bit ADC. Every sample is literally just one of 256 values (possible values 0-255). Consider an error of 0.1%: that’d be less than a single step, so wouldn’t even change the sampled value and thus wouldn’t change the waveform at all. Also, take the absolute voltage difference each step in value represents: a low end scope like the Rigol DS1054Z goes down to
1mv/div at the lowest range 4mV/div at the lowest non-software-magnified range, times 8 divisions, so the 256 values represent
8mV 32mV, thus
31.25μV 125μV per step.
A modest 5.5 digit multimeter might be 110000 counts (i.e. a dynamic range of 1:220000, since it can be positive or negative). The accuracy required is thus
vastly larger: the same 0.1% error now represents
1100 counts! As you add digits, the effort in circuit design and component quality required to achieve accuracy on your least significant digit becomes enormous. Even just the cheap 4.5 digit OWON XDM2041 you mentioned needs to discriminate 1μV per step in its lowest range —
almost 32 125 times more precise than the scope.
DMMs do part of this by being much slower. A cheap scope might measure 1 billion samples per second, while even a high end bench DMM will usually only measure up to a few thousand times per second. An 8.5 digit bench meter can take
seconds for a single measurement at the settings with the smallest error.
A cheap scope certainly requires care in design, too, due to the frequencies involved, but nonetheless doesn’t need to be particularly
accurate hardware. So you can get away with cheap components in many places. What you need is speed, and as it turns out, modern digital electronics are really good at giving us speed for cheap. So a comparatively simple analog front end feeds into comparatively inexpensive digital electronics that use fancy software to run a big screen and the accompanying buttons.
A DMM can’t really use high speed digital electronics to significantly improve its accuracy; the analog part has to get it right, right from the start, and that costs money. That analog part also generally handles much higher maximum voltages (typically ±1000V on a DMM vs ±300V on a scope).
(Some modern bench DMMs can operate somewhere in between, like the Keithley DMM6500, being able to measure 1 million times per second — but only in 16 bits, which is just 65536 different values, not the 2.4 million different values it can tell apart at slow speeds.)
Edit: Edited to reflect 2N3055’s correction regarding the Rigol’s hardware.