I'd like to note first that this is far from a perfect formula, since there are a few intangibles such as your mech type, your weapon load-out and how that factors into getting very close to 1000 weight, etc.
That being said, however, cores are one of the easiest parts to objectively evaluate, so here's a good way to evaluate their relative strength.
Almost all good mechs use heat, energy and HP modules. Using different cores allows (or requires) a different ratio of modules. For example, using the Avenger core would require more heat and energy modules and less HP modules to reach a balance. Low health cores would require the opposite. Therefore, we can come up with a somewhat objective formula for optimizing stats.
As far as modules go, the weight-to-stat-boosting ratios (for fully upgraded items) are as follows:
-HP: 7.9 per unit of weight (315/40)
-Heat/Energy: 6.2 per unit of weight
-Regen/Cooling: 4.2 per unit of weight.
In other words, you can get about 1.3 times as much HP for a unit of weight as a unit of heat, and 1.88 times as much HP as cooling or regen. This gives us a rough idea of how much each stat on a core is worth relative to the others. For instance, if one core has 50 more cooling and 50 less HP than another core, the one with the higher cooling is usually better because adding 50 HP through modules requires less weight than adding 50 cooling.
So a rough formula would be as follows:
Core HP + Heat(1.3) + Cooling(1.88) + Energy(1.3) + Regen(1.88) - Excess weight over 300(7.9)
If we plug in Windigo for example we get:
982 + 217(1.3) + 72(1.88) + 301(1.3) + 112 (1.88) = 982 + 282 + 135 + 391 + 211 = 2001 - 45(7.9) = 1645
More or less, the higher the total value, the better the core.
Here are the values of the "best" cores, roughly speaking:
Grim Reaper: 1682
Now, because I'm sure all these arguments will come up, I'll just address them here to make it easier.
How the weight plays out with your build matters a lot. Nightmare ranks the highest because it has very high stats and low weight, but if you can fit the load-out you want and have some extra weight to spare, that doesn't do you any good. Therefore, the most important thing is what fits best with your build. Naga might be "better" than Windigo, but if you've got 10 weight points to spare it's definitely not.
If modules change, the stats change. Right now mythical armor plates give more than twice as much as epic ones. If they get nerfed to say, 200 HP, cores with higher HP become much more valuable. On that same note, many players will not have access to mythical items, in which case higher HP is again more useful.
A case could also be made for some mechs to ignore energy completely and use only zero energy weapons. This certainly gives an HP advantage against non-energy mechs, and still does well against energy mechs if HP is high enough. However, Nightmare, Brutality and Windigo would still likely be the best cores in this case because they allow use of another HP module (therefore gaining another 315 HP) rather than a heat module (like a core like Avenger would need).
And yes, there are a few other factors that matter. But generally speaking, these are the best cores right now