If you look at human history the trend is that tall nations are doing better and better compared to their wide counterparts. If wide empires would be superior in a game set in the future then it means the game fails to recognize the problems they face.
Again tall empires have in the last half a millenia been much more sucessful than their wide counterparts. The neatherlands, Prussia, and the US and early UK. Compared to the french, austrians spanish and late uk (it should be noted that while the UK is strong when they are wide, their strenght is because the were tall and they basically spend that strenght on becomming wide, eventually leaving room for tall USA to usurp their poisition of global dominance.
On the face of it, this seems like an obviously true assertion, given the great divergence that reshaped geopolitics in the last half millennium. But the more I think about it, the less sure I am of it or at least the less sure I am that the tall vs wide dichotomy can be applied to the real world. Take France and the Netherlands. You note them as both tall and they were both, in terms of administrative, economic, and military policies, certainly doing the same or similar things. But I think it can be argued that France was wide in comparison to other tall European states and by the time of the Franco-Prussian War, they were soundly defeated by a state less than half their size.
Part of the problem, I think, is that government policy of economic development is a fairly recent innovation. Let's compare Tokugawa Japan and Qing China as another pair of countries that were using similar policies at the same time, but one was clearly wide and the other clearly tall by 1900. Both used, for example, mutual responsibility taxation sytems, central government inspectors to investigate corruption, mostly hands off domestic trade policies, severely restrictive foreign trade policies, and nearly full autonomy in local administrations. Both even responded to the Unequal Treaties in a similar way, up until the Meiji Restoration.
Yet well before 1900 and despite any concerted government policy to that end, Japan had a literacy rate 10 times higher than China (on par with some contemporary European countries, which is amazing when you consider the relative complexity of Japanese writing), double the effective tax rate (or more, Qing records are notoriously unreliable), and urbanization that left the least developed region of Japan as urbanized as the most developed provinces of China. Again, this is despite extremely similar government policies which can be summarized respectively as public-sponsorship for education of the literati/samurai classes while relying on private interests for everyone else; reliance on mutual responsibility groups for tax collection with intermittent inspections from the higher government; and a lack of policy or interference in the movement of peasants to the cities.
The difference it seems is less in the empires themselves than in geo-economic factors happening by themselves and in an apparent geographical or demographic constraint on administrative efficiency. It's not that the wide polities pursued a goal of width, but that they found themselves constrained by their size, nor is it that the tall polities tried to be tall, but that they were more able to adapt to the wave of (pre-)industrialization.
So what changed when governments began to take an active role in shaping their nations' economies? Everyone went tall, because at the end of the day, increasing GDP per capita or per acre increases absolute GDP and conquering more people or acreage is difficult. Looking at the nations that did try to acquire more territory in the 20th Century, you will find that the Soviet Union, the US, Nazi Germany, Communist China, Imperial Japan, and all or most of the smaller aggressors as well all tried to get taller at the same time they were getting wider. At the same time, advances in information technology allowed large countries like the US to endure the bureaucratic weight of trying to administer a rapidly growing population in the hundreds of millions just as well as smaller countries like Germany that would have had a proportional pre-industrial advantage. Perhaps the US and Germany could be called equally successful today despite the former's size.
If this can be generalized to FTL polities, then there is little reason to think they will focus on wide or tall instead of both simultaneously. The geometry of space combat also means that the fundamental limit of political strength, the optimal number of soldiers you can fit in on a battlefield, will be so large that a tallish empire would have to be quite huge itself before the wideish empire would be unable to outnumber them on any particular battlefield. I'll refrain from speculating on the implications of asymmetrical warfare in FTL polities due to holy wall of text, Batman.
