It is definitely not worth sacrificing that much INT for pittance of Piety.
The only stat you should ever sacrifice INT for is DET and usually only when you can get a solid amount of it.
http://ffxiv.ariyala.com/OX6S
Most maxed INT builds would give you about 304 DET (meeting 535 Accuracy at least). This above build would sacrifice 20 INT to gain 69 DET, which if my testing is showing in-game, DET seems far stronger post 2.4 then before. I've been doing testing with a very solid end-game SMN friend of mine, and my 20 INT vs his 34 DET and were both pulling very, very similar numbers (exact rotation), with me slightly ahead, (even with me critting more often; about 20 more times on average, mainly Festers)
I can agree that Ifrit does more damage in some places then Garuda. However, his survivalbility is lower on average as well as you spend more MP on recasting expensive DoTs /Sustain, which also increases the MP drain over a long fight. Fights where the SMN can get exclusive Ballads would probably come out more in favor of Ifrit.