You can measure with both but like the video says, often you won't get a valid result.
In lots of hardware products, you have several capacitors connected in parallel, which affects the measurement. So if one capacitor is bad, your meter will give you a value much lower than the actual esr value, because the other capacitors in parallel with that bad one mask it.
DE 5000 is a LCR meter , it does more things than just measuring the ESR. It measures inductors, resistors, measures capacitance, all at various frequencies.
The Blue ESR simply reports just one thing, an approximation of the ESR value.
If all you want is to have a tool to check if a capacitor is bad on a motherboard or power supply, the blue esr is enough.
I wouldn't buy blue esr though, it's too expensive for what it offers. I bought my esr micro for around $50, shipped, and it does the same thing.