"2000 times more powerful, recharges 1000 times faster " - so it will still take twice as long to charge it fully then?
The 1000x recharge rate means you can put the energy back in 1000x faster than the benchmark battery (e.g. 1000A x 2 hours vs. 1A x 2000 hours).
Due to the energy density being comparable, I would expect the actual size of a 2000AH New Improved[tm] lithium-ion battery would be comparable to the size of a traditional 2000AH "benchmark" battery.
Disclaimer: All the numbers made up out of thin air using values that were easy to do in my head.