You don't always need to be afraid of someone who is millions, tens of millions, or even hundreds of millions of Power more than you! Often times, new players neglect Research and most of their power consists of Troops. Troop power is not where true strength comes from.
I'm going to outline below how to compare your power vs. an enemy's power to estimate your chance at victory in a 1v1.
Scout them to find out how much Troop Power they have.
Subtract their troop power from their total power to find the sum of their Hero Power, Building Power, and Research Power.
Compare your Hero, Building, and Research power to theirs. If your's is significantly higher (this will vary greatly depending on your level) then you will probably win a battle against them. The main factors that determine the outcome of a battle are your Hero and Research compared to theirs, it's these two items that determine the majority of the strength of your entire army. Having a lot of Troops is pretty worthless if your Hero and Research aren't close to par with your enemy.
When you get to higher Watchtower levels you can get a lot of information, such as an estimate of total Troops, Troop types, specific estimate of each Troop type, and what the enemy has Researched. These will all help you judge how well you can hold up against an enemy as you grow.
When you get to higher Scouting levels you can see defending Troop count/ type approximations, reinforcing Troop type/ count/ and tier, etc. These will all help you judge how well you can hold up against an enemy as you grow.
This post was written back in the end of 2014 when power levels were a LOT lower. A high power level back then was between 50-100 mil. This article is still relevant but the separation between smaller and larger players has widened significantly. To get an understanding of what it takes to defend against some the LARGEST players, read below articles on trap accounts.
$100 Trap Account | 2 Great Rally Traps | How To Build A Great Rally Trap
Let me know how you decide if you will win versus your enemy in the comments below!
Don't forget your gems, attack boost, and VIP boosts all help out a LOT in battle as well!
Enjoy!
Navi