It really depends on your playstyle, though most of the time you should be using Path II (Explosive Arrows).
For example:
If you're trying to rush with Blaze III and while getting there you get rushed by Endermite V
Use Path I as it deals more efficiently with Endermites both coins and damage wise, this way it'll cost you less coins to defend and you'll be faster getting on track again regarding your planned Blaze III rush.
If you're in the middle of the game and get pushed by Blaze IV or V it's highly recommended to use Path II Archers.
In your consideration between Path I and II you should be thinking about, is my plan going to be focused on middle / late-game or on the early game. If it's focused on middle / late-game, investing in Path II is gonna be your choice.
If your focus is on early game AND there's a push of 2 or less waves of Blazes, you'll be going for Path I.
In the end you'll mainly be using Path II Archers as they are more effective against bigger swarms due to its area of effect.
For more information: check out the
Fast Guide!