The benefit of Extra Channel is that you "can channel energy two additional times per day".
Under Special it states "If a paladin with the ability to channel positive energy [assuming they meet the prerequisite - can channel positive energy - then this previous statement is redundant, as all paladins can channel positive energy] takes this feat, she can use lay on hands four additional times per day, but only to channel positive energy." This is not the problem, merely redundant text.
The benefit of Extra Lay on Hands is the ability to Lay on Hands two additional times per day.
Given that channeling positive energy is arguably more powerful than laying on hands (30' radius, can turn undead, takes up two uses of lay on hands [which seems to be a clear indicator that channel energy is twice as powerful as lay on hands]), these two feats seem unbalanced. One provides 2 x channel positive energy (and the 4 x lay on hands needed for same), while the other provides 2 x lay on hands.
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Channeling Positive Energy cannot turn undead without taking the "Turn Undead" feat. This is a change from the Beta. The other change from the Beta is it cannot Heal the living and Damage the undead at the same time, each burst will only do one or the other.
As to the power, they cater to different areas. While Channel Positive Energy *is* a burst heal for the same amount of damage, it does not give any of the unique Mercy cures, nor can a Paladin use it as a swift action on themself.
Let's use a 10th level Paladin as an example with a +3 charisma modifier. This paladin could use Lay on Hands a base 8 times per day.
If this Paladin took Extra Channel, he could Lay on Hands 12 times per day, but the extra 4 could only be used for Channel Positive Energy at 2 uses each.
If the Paladin took Extra Lay on Hands, he could Lay on Hands 10 times per day, but the extra 2 could be used for anything, whether it's a single extra Channel or a couple Lay on Hands.
Remember, by this point the Paladin has 3 Mercy abilities that go into effect when using the singular Lay on Hands, not the Channel Positive Energy. Also, the paladin can use a singular Lay on Hands to heal themself as a swift action, quite useful in combat.
The last main difference is in their utility against undead. While the burst can hit more of them and is better with a lot of undead, it does allow a Will save for half damage. Lay on Hands, however, is much better for single strong undead creatures. Besides only using one LoH (instead of the two Channeling requires) it does not allow a save to halve the damage. A melee touch attack is required, but a paladin should be able to make that without much worry.
They both have their uses, and each Feat serves a different purpose.
Your God of Knowledge,
Nethys
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This is my first post on paizo's board :) If I take my first level as a cleric and then take four levels of paladin with a 20 in Cha, what would be the number of channels and the amount healed per channel. If I take cleric and paladin levels seperately then I could see getting 3+cha or 8 cleric channels that only heal 1d6 and then half level of paladin +cha or 7 lay on hands which could then be used to channel three times and heal 2d6.
However, if the two channels are combined then I would get the total of 11 channels that could heal 3d6 each. In this case I would channel better as a mixed cleric/paladin than a pure cleric or a pure paladin and this seems kind of silly. I would love to get the combination but I am worried my group will frown on me for trying to powergame which they all hate. However, I could be wrong about the two possibilities and there be alternate solutions on the number of channels and the total healed
Sorry as an off topic can paladins worship abadar a lawful neutral pathfinder deity? I would love to get the bonus ten feet of movement from the travel domain for my paladin using plate armor.
Nathan
A Paladin 4/Cleric 1 with a 20 Charisma would have the following abilities regarding Channeling.
Cleric Side: Channel Energy 8/day, 1d6, DC 15 Will save.
Paladin Side: Lay on Hands 7/day, 2d6 per LoH. May Channel Energy by spending 2 uses of LoH. It would be at 2d6, DC 17 Will save.
A Paladin may worship Abadar.
Your God of Knowledge,
Nethys