Personally, I feel that arguing about the magnitude of the effect is largely pointless. The purpose of a large empire penalty is to keep small empires approximately competitive with large empires. The minimum requirement to keep small empires roughly as competitive as large empires is for the small empires to be capable of keeping up in research with large empires. This is something that the current large empire penalty completely fails to do; the most extreme situation is for the large empire to have 0% approval on all its worlds while the small empire has 100% approval on all of its worlds. In that extreme case, assuming the same average research bonus and population for colonies in both empires, the large empire will have a higher rate of research as long as it has more than 5 colonies for every 3 colonies in the small empire. This is not a very large difference in empire size; I would in fact consider these empires to be of fairly comparable sizes.
On top of that, the approval production modifier is additive with other production modifiers, such as the level bonuses of Thalan Hives, the basic effect of Economic Starbases, and the bonus granted by Interstellar Governance. This means that the relative size difference at which that 0% approval 'large' empire catches up with the 100% approval 'small' empire is less than the 5:3 colony ratio given earlier. If both the large and the small empire have a single economic starbase affecting each planet and both have Interstellar Governance, the ratio of colonies at which the 'large' empire breaks even with the 'small' empire assuming equal average research bonuses and colony population is about 3 colonies for every 2 of the small empire (each of the small empire's worlds is worth ~1.53 equivalent worlds in the large empire due to the difference in production multipliers).
The approval modifier to production fails to keep the research rate of empires which really are large in line with that of empires which really are 'small,' relatively speaking. The approval modifier keeps the research rates of empires roughly comparable in size similar, nothing more. A small empire needs to have at least comparable technology with a large empire in order to compete with the large empire in any real way. The current large empire penalty will not constrain 'large' empires sufficiently to prevent them from eclipsing the technology of the small empires for any two empires where one empire is actually 'large' by comparison to the other. The current large empire penalty therefore fails to serve its purpose.
There are ways to implement a large empire penalty that actually works. You could go directly for research rates by scaling the tech costs by the number of planets in the empire (if you have an average research per planet of R and you scale the tech costs by a factor of 1 + s*(n - 1) for an empire of n worlds, the research rate goes to a limit of 1/s times the rate of research performed by a single colony as the number of colonies goes to infinity) or by making the total empire research output be something less than the simple sum of each world's research output (say, square root of the sum of the squares, which means that an empire of n colonies producing R research per colony will research at a rate which is sqrt(n) times faster than a single colony producing R research would), or you could go for research rates indirectly, say by targeting colony expenses so that it's impractical for a large empire to have the same average research per colony as a smaller empire due to a greater need for purse worlds, or you could go for a combination of these. The current large empire penalty is sort of an attempt to indirectly target research rates, but it fails rather badly because the effect chosen will not reduce the research output of a large empire or improve the research output of a small empire by more than 25% from the nominal value (and will likely have less of an impact), and so the effect only matters for relatively small differences in empire sizes.
