A Rule of Thumb Edit
Generally, taking a gate is preferred over making a new gate when both options are equal in all other respects such as power cost, ease and efficiency, etc. This is because taking a gate means your position in the game advances, while your opponent's is diminished.
Making a new gate typically costs 4 power. This involves moving a unit for 1, then building a gate for 3.
To take someone else's gate can have a greater variety of costs. Generally speaking, if it would take more than 4 power to take a gate, building your own may be the better option. However, there are often other strategic reasons for taking a gated area that would justify spending more than 4 power. Often times, this is because the opposing player is in the lead with too many gates (especially true vs Opener of the Way who can get doom points = 3X the number of gates with their Dragon Descending spellbook). Other reasons could include attacking an enemy Great Old one with Nyarlathotep, or getting kills in combat with Great Cthulhu.
Carpe Diem - Seize the
Day Gate Edit
In most games, there will be many times when you can take a gate for less than 4 power. This is when you should focus on taking a gate, rather than building your own. Look for these opportunities and seize them when they arise. Many factions have a variety of tools to accomplish this.
A very common tactic that any faction can use is to move a Great Old One and a Cultist into an area with only one cultist. You can then capture the existing cultists off o the gate and replace it with your own. Try to do this when the enemy is out of power to prevent them from declaring combat or summoning more defenses.
(This page is a rewritten version of Aurthur Petersen's post found here )