In industry, ultrasonic welders are used for joining pouch cell tabs most commonly, with relatively slow-ish resistive heating welding being sometimes used in conjunction with ultrasonic welding. A123 used a special powder metal laser welding method which had relatively high fall-out (there is good reason that's not the industry standard method).
As far as welding highly conductive foils with a capacitive discharge welder reliably, good luck. The current densities needed to flash copper foils to molten typically will also have such strong magnetic fields the molten material splatters from localized magnetic repulsion. At least that's how my experiences with it went, if you turn the energy dump up enough to really melt the metal, it splatters, if you decrease the energy, it just makes a joint that visually looks like a weld, but you can knock the weld apart with a brush of your pinky.
My favorite method for joining foils is mechanically crimping. When done right, ultra-low resistance, excellent mechanical strength, and the lack of heat/arcing involved make for good quick easy joints that don't require special equipment beyond a crimper for under-floor heating foil connections.
