Short Answer: it all depends on your AHJ.
Longer Answer: It depends on what you're trying to do. If you're doing anything grid-tied, it will most likely require full UL listing by your utility, and it may also require to be on their certified equipment list. If you're just trying to power a well-pump for your off-grid cabin in the woods but your insurance needs something permitted, then your local AHJ may accept TUV.
UL Listing usually requires better fire protection. EG4 batteries got reworked to add in more safety/fire protections to start their UL certification process. The higher-end UL listed stuff (Sol-Ark, Schneider, etc.) have built in safety protections like arc-fault detection, and other safety means that the TUV-listed equipment (EG4, Growatt, MPP/Voltronic) stuff doesn't. You'll also see here on this forum that plenty of TUV-listed stuff has failed or burned up, but I have yet to see anything like that on a fully UL-Listed product.