If I put up permancey arcane sight the incremental benefit of putting up permancey detect magic and permancey enchantment sight looks minor. Is there a good reason to spend the extra gold to get permancey detect magic or enchantment sight if you know you will get permancey arcane sight?
Detect magic gives you no benefit if you already have arcane sight. It has a shorter range and requires concentration. It is limited to a cone so you may not be able to detect everything you can see.
Enchantment sight is more limited as it only detects enchantments but has the benefit of allowing you to get a lot of information without any rolls. It even allows you to determine the precise sub-school of the effect. With a spell craft roll you can determine the exact level of the spell instead of just the strength of the aura.
So, how valuable enchantment sight is going to be is going to depend on the character. To determine the school of magic with arcane sight requires a knowledge arcane roll of 15 +. You can only make an untrained knowledge skill if the DC is 10 or lower. That mean anyone who is not trained in knowledge arcane cannot even attempt to determine the school. If the character is a wizard, chances are they are trained in knowledge arcane and probably have a good roll as well. That is going to reduce the value of enchantment sight. For a caster who is not trained in knowledge arcane, or who has a low roll it may be worth it.
Enchantment sight came out after the core rule book so it does not say if it can be made permanent on a target other than the caster. If it can that would be one reason to use it instead of arcane sight.