I'm running Ubuntu MATE 16.04.3 LTS on a Thinkpad T430 (Core i7 dual-core, nominal 2.9 GHz clock, 8 GB RAM, 9-cell internal battery and 9-cell Slice battery). My battery life is excellent, as much as 10 hours of normal use on a full charge.
I recently had performance issues playing a game (Kerbal Space Program) on AC power, and found that the computer had been left in Power Saving mode, causing the CPU to run at lower clock speed than is necessary when I'm not trying to aggressively conserve energy. This probably occurred before I purchased the extended batteries, when I was trying to aggressively increase battery life with the original 6-cell battery.
I can easily switch the CPU back into Performance mode using the CPU Frequency Scaling Monitor widget that I've mounted in the system bar (which appears to separately control clock management for the two real and two virtual cores) -- but I've examined the Power window of system settings and don't see any way to tell the OS to automatically switch between Power Saving (which I'd want when on battery power) and Performance (which I'd prefer when on AC power).
I hope I'm just missing something obvious; I'm fairly new to 16.04 and to MATE, having just gotten this machine (and clean installed Ubuntu, reluctantly keeping Windows 10 on dual boot) a couple months ago.
A search for similar questions turned up this one, which seems similar but refers to Ubuntu 14.10, now EOL, and may or may not be correct for my exact hardware even so (I'm not certain how to tell if I have a Sandy Bridge CPU).