“Warning spoiler alert”
I’ve read most of the prime timeline books from next generation, voyager, titan, ds9 and the Typhon pact etc. The trek story is well evolved and developed in the book series. I recommend them as they explain answers not only to this question but lots of others as well, like the origin of the Borg as example. Now to who would be more powerful? I guess this would depend on when. So let’s just start in the late 24th century early 25th century. By this era the federation is the undisputed super power of the alpha quadrant and one of the major powers in the entire galaxy. They not only have the raw resources since their territory is the most vast of all alpha quadrant powers. In the late 24th century it’s over 8000ly wide and 2000ly deep. But it’s not just geography, ships or the technology alone. The Federation seems to have struck just the right balance of all aspects of a successful civilization. One that is destin to encompass the Milky Way galaxy (Q). The Federation also has the security, freedom and liberty necessary for every citizen to reach their maximum potential with no barriers or class structures. But it is designed around allowing the individual being given the tools, the opportunity and the choice to develop into whatever they desire. This has fostered the most productive and happy citizens possible. Certainly the most productive, fruitful, rich and diverse society in the Milky Way. Allowing all the intellectual resources from all their member worlds and allies to work together efficiently and seamlessly with little to no barriers to achieve successe. Thus this model maximizes problem solving and technological advancement that moves at a much faster pace as opposed to closed rigid totalitarian societies like the breen, romulan Kazan, or the tzhencathe. And since they have trillions of citizens along with hundreds of member worlds and powers that encompass nearly an astonishing 100,000 star systems. Thus Enabling them to exploit enormously vast amounts of hard, soft, Biological and intellectuall resources. Giving the federation the ability to manufacture materials, products and ships at a astonishing rate, akin to the US in WWII. By 2950’s the federation Starfleet consisted of over 75,000 capital star ships and space stations. And a merchant fleet nearly a astonishing number of 150 million merchant vessels. Tacticaly their technology in this era gives them a huge edge to most all rivals. For example the federation has perfected quatum slipstream drive which is faster than the Borg trans warp, making a trip to the delta quadrant in a matter of hours to a couple days. Tacticaly their space stations and vessels have a regenerative abalative and atomically regenerative nanite driven reactive type armor similar to the armor seen in the last voyager episode. They use multiphasic,regenerative,temporal type shielding, reinforced by zero point dark energy fed into the shield matrix via magnetic energetic particle transfer. These shields are designed to stand up to the most lethal threat weaponry including the Borg. This is amongst the most resilient sub space graviton shielding in the known galaxy. Their ships have the best sensors capable of analyzing subatomic particles and energies vast distances, in some cases tens of thousands of light years. The federation and allies share the fastest artificial computing power yet designed. ComputE cores with hexagonal UHFTL quantum entangled tunneling methods. These sub atomic compute cores are made of self replicating particle lattice structures capable of “real time fuzzy logic sentients”. Coupled and Synergized with the very latest non sentient HFTL Bio neural technology. Giving such equipped systems unprecedented computing power capable of solving the most challenging technical and cosmological problems of our scientist with highest possible accuracy and precision. Their medical sciences are also the most advanced among the alpha quadrants powers. Humans for example can live up to an estimated 900 years. Their ships now have holographic crews that can activate and repair the ship via particle synthesis (Caliear/Borg technology) as well as act as holographic doctors or command personnel if the crew is killed or incapacitated. By this era the federation even sends a small fleet to the delta quadrant that proved more than a match for the devor and even the mighty voth got tought a lesson in the right way to conduct peaceful and fruitful negotiations. They also have some of the most powerful weapons. They still use phasers, pulse cannons and several types of torpedoes like quantum and transphasic torpedos. Weapons like the transphasic torpedo penetrates all known threat shields due to the weapon being “out of phase” with normal matter. This is similar to the krenim weapons In voyager but operate by oscillating both nutational phase state and dimensional amplification thus allowing them to not only penitrate threat vessel shielding but it also does not allow for easy or effective countermeasures or easy threat counter adaptation. They can also apply this type of modification to their beam weapons, particle cannons, phasers, plasma weapons and so forth. This made them very effective against threats the Borg (b4 Caliear transformation to the gestalt) and to species 8472 technology (b4 treaty of Boktu Krat) as well as other high technology and high threat species.They also can field other types weapons one example would be protomater, dark matter and vorzanuim based weapons. But these weapons are of such magnitudes they are rarely used and not generally fielded due to the hazzards not just to the enemy, but the delivery vehicle or vessel, and any friendly forces or even to nearby inhabited Star Sytems or space stations that is in the effective blast radius. The aforementioned weapons makes the federation and allies very formidable opponents to just about any threat species or vessel. By this time they also have developed a type cloaking technology that they call “ ultra low obserabilty or stealth”, technology similar to but in many ways rivals Romulan cloaking abilities most notably in its lower power Requirments and countermeasure detectabilty. Federation ships in this era are very advanced and are among the most powerful of all major powers. Another thing that makes them very strong is they have a lot of allies, very powerful allies united in a pact called the kitomer powers. During this time they have allies like the cardasian, xindi, ferengi, Klingons, the Gama quadrant dominion and the delta quadrant confederacy to name a few of the big ones, They all belong to a alliance called the kitomer accords. The aforementioned Delta quadrant ally the Confederacy is almost as large as the alpha quadrant federation but not quit advanced technologicaly. Their are many other smaller allies or regional powers about like Lyrans, citazians, tellurians, moxobara and the bodea just to name a few. In the delta quadrant, the federation has allies such as the trabe, hirogen, krenim and the zohl. Even the first federation member in the delta quadrant, the telaxians from telax prime.
They also have intimate knowledge of “caliear” and their technology. The Caliear is the most advanced civilization in the entire galaxy, if not our entire galactic super cluster. This technology was able to humble the Borg as easily as a Q snapping of a finger. In the future (beyond the 29th century) this technology gives them access to cool abilities controlling temporal and dimensional energies which they begin to field portals like the iconians. Side note the books also reveal what happend to the iconians. Hint it has something to do with Q. By the start of the 25th century they begin to create artificial wormholes by quantum stepping a element called “Corzanuim” out of small low mass singularities known to us now as black holes. They even can harness the energies of the omega particle by the late 31st century (Caliar tech). This is why the Q are so interested in the federation. The federation gains knowledge and power very, very rapidly uniting thousands of species and empires in a common peaceful political and economic organ. The Q know this future and are behind the scenes helping to guide them in the right direction, this also is keeping the timeline intact, (in our dimensional plane of coarse). By the 29th century the federation spans the Milky Way galaxy, and becomes the preeminent power. With most civilizations in the galaxy belonging to the federation by the 30th century. All I can say is read the books they are amazing if your into Trek. There’s so much in the books I would never be able to add it here but I tried to give as many examples as possible. Let me know what you think. Especially anyone who reads prom timeline books.p