Arleigh Burke-Class Destroyer:
Length = 155m
Width = 20m
Height = 9.3m
Mass = 9,200,000kg
Volume = 155*20*9.3 = 28,830m^3
L/W Ratio = 7.75
L/H Ratio = 16.66
Paragon Industries Frigate
Length = 100m
Width = 12.9m
Height = 6m
Volume = 100*12.9*6 = 7,740m^3
Surface Area = 2*100*12.9 + 2*12.9*6 + 2*100*6 = 2,580 + 154.8 + 1,200 = 3,934.8m^2
Assuming 25% of the ships hull is covered in radiator strips and that thanks to Paragon Industries' Advanced Materials they can reach a temperature of 2,500 C compared to the normal 2,000 C.
Thermal Radiation = 0.00000005670373 * (3,934.8 * 25%) * 2773.15^4
Thermal Radiation = 0.00000005670373 * 983.7 * 59141651118315.05100625
Thermal Radiation = 3,298,889,316 Watts
Thermal Radiation = 3,299MW
Now this does assume that the radiators are blackbodies but I have no idea how they would compare to the ideal blackbody radiators so I'm just going to assume they are for convenience sake.
As detailed earlier a PI Frigate using current tech is 88% efficient so given the maximum sustainable output of heat we can work out the total reactor power.
Power = 3,298,889,316 / 12%
Power = 27,490,744,300W
Power = 27,491MW
That's 8,247MW each for Weapons, Engines and Eezo and 2,749MW for all the other systems.
For comparison A Los Angeles-Class submarine has a peak power output of 190MW, the Hoover Dam has a peak power output of 2,074MW, and the World's Largest Nuclear Power Plant has a peak power of 8,210MW
Meanwhile a similarly sized regular Alliance ship would have a thermal radiation of:
Thermal Radiation = 0.00000005670373 * (3,934.8 * 25%) * 2273.15^4
Thermal Radiation = 0.00000005670373 * 983.7 * 26700068717603.30100625
Thermal Radiation = 1,489,315,394W
Thermal Radiation = 1,489MW
Now while earlier I calculated the thermal efficiency of an Alliance ship at 67.44% but that's during combat. Outside of combat it has an efficiency of 68.85%. From that we can determine it would have a reactor of:
Power = 1,489,315,394 / 31.15%
Power = 4,781,108,809W
Power = 4,781MW
So thanks to it's better materials and more efficient engines and reactor not only does the PI Frigate have an effectively unlimited combat endurance it's also 5.75 times more powerful (in the literal sense).
Thanks to this increased power outside of combat its engines 5.75x more powerful and almost certainly at least that much faster. Given the decrease in mass thanks to the Arc Reactor and Repulsors been smaller then their equivalents and lower mass armour with the same protection the PI Frigate would, right now, almost certainly be six to seven times faster then an equivalent Alliance frigate. More if you factor in that the Eezo core would also be receiving almost six times more power.
And while this increase in speed sounds nice what makes it terrifying, for the Aliens anyway, is what that really means for the Alliance. The Reapers can go 30LY/Day and with the Citadel Races half that they can do 15LY/Day or 0.625LY/Hr.
With an Average of 50 hours of FTL before a discharge is needed they can cover 31.25LY. Of course they can actually go that far since they need to ensure they are within range of a discharge location when their time runs out. With the increased engine power and core power I figure our Frigate could squeeze out at least 5x the sustained speed, 3.125LY/Hr. That gives it a range of 156.25LY.
To put that into perspective there are five stars within 31LY of Earth with confirmed planets but (about) sixty within 156LY. I can think of numerous advantages to been able to lay claim to solar systems no one else can reach for the Alliance. Everything from secure military/research bases to previously untouched reserves of Eezo to safer garden worlds.
Then there are the weapons. Now we know that the size of accelerators on ME ships are in part due to recoil ripping the weapon from it's mount however we can still put this additional power to use.
Normally a Frigate like this would have one main gun ~80m long. Instead we could mount 4x 80m guns, two on each side Defiant Style, each of which would have 1443MW compared to the standard 1004MW. This 40% increase in power can likely be dealt with thanks to our Advanced Materials allowing us to build better connections thus increasing the recoil it can take.