3 year old batteries were slowing down mine and the wife's IPhones (6 & 6P models).
Did my IPhone 6 Plus first, two of the three white sticky strips under the battery snapped off while trying to remove the battery so I have to pry out the old battery using the plastic tools. At one point the battery case broke open and small flame and smoke came out but I was able to get it out without further incident. Installing the new battery was easy except for the four ribbon cables in the upper right corner, the middle one caused the most issues and I had to reseat the cables three times before they were connected correctly.
My wife's model 6 went a little more smooth, only one battery sticky strip snapped off during removal and I only had to pry a little. Still the same issue with reattaching the ribbon cables.
Other than that the new batteries are working great and our phones are much faster now and hold a charge for about 3 days.
Take your time, be careful, have a bright work light and a magnifying glass on hand because you can barely see those microscopic screws.
A magnetic screw dish is also handy for those tiny screws so they don't get lost, can get one at Lowes.