There are two aspects that you need to consider here: One is physical measurement of luminance, luminous flux, or illuminance (I'll come on to the differences in a moment), and the other is the much less clear-cut issue of human perception.
Let's deal with the physics first. There are three concepts to explain, which are all related:
Luminous flux is the total amount of light emitted by a light source, in all directions. Its SI unit is lumens. This is difficult to measure without expensive equipment (an integrating sphere). Luminous flux is relevant because it gives a measure of the total amount of light that a source is putting into a room, and will typically be given in the specifications of a light source.
Illuminance is the amount of light that falls on a surface of unit area. Its SI unit is lux, where 1 lux = 1 lm/m2. It is easy to measure with commonly available "light meters" and photodiodes. Illuminance is the most important value when asking, for example, "will enough light fall on this desk for somebody to work by". Building codes or standards often specify the illuminance required on floors, walls, or work surfaces, for specific tasks. This is a function of the overall design of lighting in the space rather than just of the light source - type of fixture, quantity and spacing, colour of the walls, etc., are all important - but marketing materials for some LED light sources in particular will claim "equivalent to xxx wattage incandescent" by comparing the illuminance on a small area of work surface from an omnidirectional incandescent lamp vs a narrow-beam LED, and imply that they are equivalent - despite them having radically different effects everywhere else in the room.
Luminance is a measure of the amount of light being given off by a surface in a specific direction, per unit of area. If that surface is the surface of a light source - e.g. if you look at a light bulb - then this is related to how bright the source appears. This measurement is relevant because if a customer looks directly at a range of light sources to compare "how bright they are", it is differences in luminance that they will see. Luminance meters are much more expensive than illuminance meters.
So in summary,
- Luminous flux is the total amount of light given off by a source
- Illuminance is how brightly a surface is lit
- Luminance is (part of) how bright the light source appears to the eye
Which one(s) you need to measure will depend on exactly what you are trying to achieve.
Human perception is the tricky part here. There is more to a feeling of "brightness" than either of the measures above. For example, people tend to perceive light of a higher colour temperature as being brighter than light of a lower colour temperature - a common issue when comparing LEDs to other sources. People are also strongly influenced by contrast; we mostly see relative rather than absolute brightness, so a patch of light on a small area of workspace in an otherwise dark room may seem brighter than the same illuminance throughout the space, especially once the viewer's eyes have adapted to the dark. So be very careful if giving practical demonstrations, or you may find that the customer's perception does not match your calculations.
(it's also worth noting, of course, that for some purposes it's the perception that matters...)