I know this has all been asked before but I've not been able to find a nice definitive source on this stuff. Here is what I've gathered, please let me know if I have anything wrong.
NEC Backup BoosterNEC's own memory system
-- 2k of memory
-- has AV output as well, basically the Japanese version of the TurboBooster Plus (listed below)
Ten no Koe 2A small, plastic add on, functionally equivalent to the US TurboBooster Plus except no AV support
-- Created by Hudson, beat out the Backup Booster because it was cheaper
-- Has 2K of internal memory (which is what the '2' in the name denotes)
-- Uses 2 AA batteries
-- Works on original PCE, Core Grafx, Core Grafx II and SuperGrafx
-- Insert any system card and hit select to access the memory manager
-- Takes over the expansion port, denying use of the AV Booster for the original PCE (thus, RF only)
Ten no Koe Bank HuCardsHuCards that have 8k of memory on them
-- Only needed if you want to transfer your saves from machine to machine, or temporarily store a save on the card
-- The saves on the card itself can't be used again until transfered onto a machine
-- The card contains batteries
-- Works with the US Duo, TG16 CD add-on and TurboBooster Plus assuming your system can load Japanese HuCards
-- Has four 2k banks, you can only swap a bank at a time, not individual files
Shuttle Memory Backup UnitSimilar to the Ten no Koe 2, but only works on a PCE Shuttle
-- uses a rechargeable lithium battery to store its saves
-- Still available brand new from NCSX for about $38
PCE IFU-30 ("Suitcase style") CD Add-on-- 2k of memory
-- Uses a charged capacitor
-- should turn on system at least every 2 weeks to maintain saves
-- Compatible with Ten no Koe Bank HuCards
Super CD-Rom2 Add-on-- 2k of memory
-- Uses a charged capacitor
-- should turn on system at least every 2 weeks to maintain saves
-- Compatible with Ten no Koe Bank HuCards
Duos (US, Original PCE, R and RX)-- 2k of memory
-- uses a charged capacitor to save the data
-- should turn on system at least every 2 weeks to maintain saves
-- Compatible with Ten no Koe Bank HuCards
Turbo Grafx CD Add-on-- 2k of memory
-- Uses a charged capacitor to save the data
-- should turn on system at least every 2 weeks to maintain saves
-- Compatible with Ten no Koe Bank HuCards (assuming your system has means to run Japanese HuCards)
TurboBooster Plus-- For use on the TG16 only
-- Has 2K of internal memory
-- uses a charged capacitor to save the data
-- should turn on system every 2 weeks to maintain saves
-- Compatible with Ten no Koe Bank HuCards (assuming your system has means to run Japanese HuCards)
-- Can NOT use a system card to manage save files (seems like it might partially work? formatting?)
-- Can access and manage files using an in game manager, such as in Order of the Griffon
TurboBoosterJust has AV, no memory support
Memory Base 128-- late RPGs would consume most/all of the 2K available in existing save systems, so the MB128 was the answer
-- has 128K of memory, 64 times more than previous systems
-- connects between the controller port and controller
-- will work on a US TurboDuo as is
-- will work on a TG16 if a controller adapter is used
-- runs on 4 AA batteries
-- Games must support the Memory Base 128 specifically (about 18 games in total, see below)
-- Popful Mail has a rather nice interface for managing your MB128 data
-- Koei Strategy games require the MB128 for saves (I guess their save data is larger than 2k?)
Memory Base 128 compatible gamesDetailed list here:
https://www.pcenginefx.com/forums/index.php?topic=764.0A-Ressha de Ikko- 3
Aoki O-kami to Shiroki Mejika [Save-kun]
Atlas (the) - Renaissance Voyager
Brandish
Eikan Wa Kimini
Emerald Dragon
Fire Pro Female Wrestling (WOWOW vs. JWP)
Magicoal
Linda Cube
Nobunaga no Yabo-: Budo- Fu-un Roku [Save-kun]
Nobunaga no Yabo-: Zenkoku Ban [Save-kun]
Popful Mail
Princess Maker 2
Private Eye Doll
Super Real Mahjong P II & III Custom
Super Real Mahjong P V Custom
Tadaima Yu-sha Boshu-chu
Vasteel 2
Koei's SanGokuShi III (Romance of the Three Kingdoms III)
Save-KunA save system that Koei made specifically for their games
-- basically a clone of the MB128 and compatible with MB128 games
LinksGreat write up on the Ten no Koe 2 --
http://magweasel.com/2011/04/29/i-love-the-pc-engine-tennokoe-2/Nice review of the MB128 --
Some info on the Save-Kun --
https://www.pcenginefx.com/forums/index.php?topic=4257.5More detailed info on the MB128 --
https://www.pcenginefx.com/forums/index.php?topic=615.msg3341#msg3341Detailed list of MB128 compatible games --
https://www.pcenginefx.com/forums/index.php?topic=764.0