When I exchanged my sim card, it did help with dropped calls and signal strength, but it did not improve my battery life. It may help some who are experiencing battery issues. It may have helped some in my case because after reading forums, it seems like I never had good battery life, and the ji6 update just made it much worse.
The problems people are having post update may have shed light on some peoples unrelated battery problems which were solved by new batteries, sim, or settings. But the post update issue is very real and the only thing that solved it for me was a warranty exchange.
I am now able to get through a work day even with heavy use. Saturday with light use I still had 75% or so left after a solid 24 hours.
And.. No, my new sim card looks the same.