For LVM -> http://tldp.org/HOWTO/LVM-HOWTO/whatislvm.html
I'm not 100% sure about the encryption as I have not utilized the Ubuntu one. However, I did use the Manjaro one with identical text and it involved full disk encryption (encrypts everything but /boot)
This requires typing in a password to unlock the disk and then proceeds like a normal OS (requiring another password to login)
This is similar to my LUKS encryption of /home, .encryptfs however does not require multiple passwords. If this is more or less secure depends on whom you ask.
I guess you'd maintain similar security if you used autologin and the full disk encryptio option as you would with full disk encryptio and normal password login?
Which encryption method would have less of an overhead? Would it significantly slow down a 6 year old laptop 80GB HDD, 1GB RAM vs no encryption?
Are those 2 installation encrpytion methods safe from someone enter Linux recovery mode?
Edit: "On September 2013, Phoronix published a benchmark comparing performance between LUKS and eCryptfs. They used Ubuntu 13.10 (latest available at that time) and they obtained better results encrypting the whole disk using LUKS than encrypting just the user home using eCryptfs." from http://en.wikipedia.org/wiki/Linux_Unified_Key_Setup