I had a bit time now to look at apps for data logging. This is the one i use mostly:
http://appcrawlr.com/ios/barometer-altimeter-for-iphone-
It has an old fashion interface that works well as barometer/altimeter. It doesn’t seem to be to tough on the battery. It also has data logging but this function is useless since it only collects data when active on the screen, and I haven’t found any settings to change that. It has not really been a problem though since I normally use my Kestrel for data logging. More battery efficient, whether resistant and I can get temperature, humidity, wind etc.
Looking now at data logging apps, this one can log barometer values but that is (almost) the only thing it can do, love it or hate it:
http://appcrawlr.com/ios/barograph-a-barometer-and-altim#authors-description
It works. I have no idea of battery drainage.
Barometer plus seems to have a working graph and settings where you can control data logging interval, set reference altitude, and even fine-tune calibration if have a good reference instrument. I have only used it a few minutes now but it seems to be a good (free) app
https://itunes.apple.com/us/app/barometer-plus-free-altimeter-and-barometer/id1071044152?mt=8
Being able to control data logging interval should hopefully help to mitigate battery drainage.
There apps that combines temperature, pressure and even humidity. Sounds great but I doubt it works well, Iphones have what I understand no humidity sensor and I have never managed to get good temperature reading out of a phone, it tends to generate its own microclimate. There are also loads of weather predicting apps that can show pressure, I think most of them require access to internet to work well but I haven’t looked into them. Many of them get good user ratings.
Btw if you have an Iphone 6 it could be worth testing, it should have a pressure sensor as well, but I don’t know about the quality.