i see it two ways. the build is stronger than any house for sure - because the guild is all focussed on warfare, while the houses are focussed not only on warfare but mostly on social affairs - civilian duties, politics etc.
think of it like a slider showing percentages. - lets say, the guild puts 80% of its resources to shipbuilding and pilot/crew training and 20% to research. - at the same time, liberty puts 5% on shipbuilding and 7% on research. - the result is that the guild deploys a larger fleet and better equipped pilots. - but - they have hardly any room to expand it. - liberty on the other hand can shift their resources - they cut the civil service and reduce its social duties ( as often its done in times of war ) - and move their resources towards warfare and end up with like 10% shipbuilding and 20% research - and since they have a much larger pool of resources to take from - they ll have more - and can - if needed still expand.
but - if there is no war, they don t need to.... so it comes to the fact ( which is nothing but a guess ) that the BHG has the largest lawful fleet, but hardly room to expand it at a greater rate than they allready do.
furthermore, the BHG is most of all that... lawful. they have no interest in taking over house space - and they try hard to take over gamma and alpha. - if they were not fighting the nomad war - and had still deployed their warships - the corsairs or outcasts might be in greater trouble, but atm, the guild fights on multiple frontiers. - so its in the corsairs / outcasts best interest to keep the guild busy with the nomads and the order. its a bit like the zoners trying to ensure that corsairs and outcasts will never make peace.
some things are still undiscovered. - the guild produces a lot of warships - maybe as many as rheinland who are rebuilding their fleet. - but its nowhere said where they get the materials from. there is no lore about any dealings with cooperations. its not the zoners - they don t fly to the BHG bases much. so - a lot of lore is lacking when it comes to the factions.
but the most important thing about the guild is - they do not possess a planet as a base, but only stations. so they don t have a real base. a faction like that could never compete with a houseforce truely - but they can be strong enough to discourage any house from acting against them for sure. - but thats no question here, cause the houses and the BHG get on well - cause they depend on each other.