In the above example (consumer 70-300 [often f4.0-5.6], vs pro 70-200 [usually f2.8]), when these lenses are placed on the same cameras, the pro 70-200 will give 4x the light compared to f5.6, or 2x the light compared with f4.0 (consumer zooms are often variable aperture, while pro lenses are more frequently constant aperture). If you were to compare the pro lens on some camera, and the consumer lens on some different sized sensor, the math can get more complicated. Below is an explanation of what f-stops mean, if you're interested.
the maximum f-stop of the lens describes the ratio of sensor length (1D, diagonally is best comparison probably), to the diameter of lens aperture. because the opening and sensor are two dimensional, every sqrt(2) increase in f-stop describes halving the light. for example, a f 1.4 lens can allow ~twice as much light as an f 2.0 lens. Every doubling of light is considered a "stop", like {1.4, 2.0, 2.8, 4.0, 5.6, 8.0}. An important consideration is that this number describes a ratio, not the absolute opening in the lens without respect to sensor size.
One possible conversion method is to consider the sensor size of the system against some popular standard. For example, "aps-c" sized sensors are about 1 stop "slower" than full frame sensors, due to being 1/(2.25) the size of full frame sensors in area, or 1/(1.5) linearly. This means that many lenses can be converted not only on focal length, but also for f-stop, to estimate the total light gathering power of the system, and the output "look" of the image. Full frame sensors (~36mm x 24mm) are most frequently used in the photography world as a standard comparison point. For example, a 50mm 1.4 lens gives 50mm 1.4 on full frame, but that same lens on an aps-c sensor (like a fuji X, sony 6xxx, canon 7d, etc.) would not only give a cropped 75mm [full frame] focal length equivalence, it would also give the depth of field of a 75mm _2.0_ lens [on full frame], not 75mm 1.4. At the same time, the exposure would still benefit from the light gathered at f1.4. This is why many say that smaller sensors give a larger depth of field (more in focus, less out of focus background). In reality, this is due to the lens aperture being measured only as a ratio to the sensor size. Finally, the smaller aps-c sensor will give a larger depth of field at the same f stop, but may also give higher noise at the same ISO (to a similarly advanced full frame sensor). This means that an aps-c camera takes the exact same image when it has ~1 more f stop, ~33% less focal length, ~1 stop lower ISO to the full frame system. A big confusion around any of this "equivalence" discussion is that sometimes people mean equivalence for lens "look", and other times, they mean equivalence for exposure, while others may be talking about absolute image quality and noise. They're actually all related, though much of this discussion isn't important to real world photography.