GunLvrNLearner,
I really enjoy your questions, but I have some very respectful advice for you.
Become familiar with
www.handloads.com and various ammo mfg websites. I like Double Tap. Comparing energies in various loads from different sites will be more factual than the answers you get here. (Before everyone else get's offended, this includes my answers. We all have bias.)
The definition of 'power' is variable when comparing cartridges. Power as in raw energy (at the muzzle, 25 yards, 100 yards), power to penetrate (phone books, ballistics gelatin, flesh, bones, steel, concrete blocks), etc.
And the answers can be very different. Bullet diameter, construction, sectional density all play a role in how a given bullet behaves terminally, and effect this concept of power. Ballistics coeffecients will effect how much muzzle energy is preserved at distance. (This is usually not a significant factor in common handgun calibers...they all fly like bricks.)
For instance, the 5.7X28 has roughly half the energy of either the 357 Mag or the 10mm. However, the 5.7 will consistenly penetrate body armor with steel penetrator, aluminum core (SS190) ammo. Neither of the other rounds will.
To your original question, the 10mm Auto is roughly 15% to 25% more powerful than the 357 sig. The 357 Sig is roughly 4¢ per shot cheaper than the 10mm from Georgia Arms. It will also be cheaper to reload due to both lower material requirements to create the lighter bullets and smaller case capacity. New brass is .8¢ more than 10mm, due to the extra operation in creating the case shoulder (starline brass).