Shadow Pidgeot

Shadow Pidgeot is a marked improvement over its basic forme, but it's also a very mediocre Pokemon. It can work as a Flying Type attacker, but it's outclassed by even some non-shadow, non-Legendary Flying Type attackers. Honestly, if you manage to get one with high enough IVs, then it might be worth purifying for a high-IV Mega Pidgeot.

Best PvE Offensive Moveset

• Gust* and Brave Bird provide maximum damage
• Wing Attack* is second best, Air Slash is... non-elite.
• Steel Wing is worthless on Shadow Pidgeot
• Hurricane is the second best charged move, followed by Aerial Ace, then Air Cutter.
• Feather Dance is worthless for PvE. 

Best PvE Defensive Moveset

• Gust* provides huge power on defense, but it's the same type as all of Pidgeot's charged moves. Steel Wing is also decent, though its coverage is fairly similar.
• Air Slash is an okay secondary pick if you don't have a Shadow Pidgeot with Gust, but it is definitely weaker.
• Wing Attack* has no defensive viability for Shadow Pidgeot
• Aerial Ace is the top choice, as it comes out frequently
• Air Cutter is only slightly stronger than Aerial Ace, but the energy requirement is too high to make the trade-off worth it.
• Brave Bird is the best one-bar move, but Shadow Pidgeot may never use it.
• Hurricane is a weaker Brave Bird.
• Feather Dance is worthless for PvE. 

Gust is the most ideal for Pidgeot, sporting the strongest damage output while still returning respectable energy gains. Wing Attack is generally inferior, but offers slightly superior energy generation, resulting in quicker access to charge moves. Air Slash is weaker to Gust, and should only be chosen if you lack Elite TMs.  

Brave Bird is the most efficient and powerful charge move available, though it's also risky with its significant self-debuff. Hurricane costs the most energy and is not worth the cost, while Air Cutter is just a horrible move overall. Contrary to regular Pidgeot, Shadow Pidgeot may prefer Aerial Ace for its low cost, as it is less bulky and doesn't make as great of a use for Feather Dance's debuff.