To answer your questions:
Yes they are more precise than anything else I have encountered (in 20+ years).
Yes they are well worth the effort. You can estimate size, resources, quality and schedule from just the FP count - extremely useful. It takes an average of 1 minute to count an FP manually and an average of 8 hours to fully code an FP (approximately $800 worth). Consider the carpenter's saying of "measure twice cut once". And now a shameless plug: with https://www.ScopeMaster.com you can measure 1 FP per second, and you don't need to learn how!
I like Cosmic Function Points (because they are versatile) and IFPUG because there is a lot of published data (mostly from Capers Jones).
Having invested considerable time, effort and money in developing a tool that counts FPs automatically from requirements, I shall never have to do it manually again!