Well, as discussed in the comments, the first thing to consider is that STAB brings thunderbolt to 135 rather than 180.
Second, there are more type combinations to consider than just those that result would give rock a x4 multiplier. Especially considering rock and electric share a x2 against flying.
Times when using Ancient Power is more effective than Thunderbolt (used by an electric type):
Immune to electric (x0)
Ground or Ground/anything also Lightning Rod
While rock isn't good offensively against ground either (x0.5) - ground is completely immune to electric. As is any Pokemon with the Lightning Rod ability. Lightning rod may also affect your usage of Thunderbolt in double or triple battles, if one opposing Pokemon has Lightning Rod, you do not want to use electric against either target.
Super resistant to electric (x0.25)
Dual types of consisting of two of (Dragon/Electric/Grass)
This category is rare. As there are no Dragon/Grass Pokemon, the list here is made up entirely by Mega Ampharos, Zekrom, and Rotom(Mow). Although rare, these three would effectively reduce Thunderbolt's power to ~33.75
Resistant to Electric (x0.5) and weak to Rock (x2)
Any dual types that combine one of (Dragon/Electric/Grass) with one of (Bug/Fire/Ice)
Paras, Parasect, Wormadam(grass), Sewaddle, Swadloon, Leavanny, Joltik, Galvantula, Mega Charizard X, Rotom(heat), Rechiram, Snowver, Abomasnow, Rotom(frost), Kyurem.
In this Category, Tunderbolt's power would be 67.5 vs Ancient Power's 120.
Double effective Rock (x4) and neutral to electric (x1)
Dual types of consisting of two of (Bug/Fire/Ice)
Another rare category, made up entirely by the two Bug/Fire types. Here Ancient Power would do 240 vs Tunderbolt's 135. This category does not include the Flying type, as flying is also weak to electric which would cause thunderbolt to jump to 270.