The differences between Gold Uhura and Red Uhura are nothing compared to the difference between Uhura Prime and NuUhura. Could they be any more polar opposites?
Try to imagine Nichelle Nichols saying “Who’s the mouth-breather hiding under your bed” or “I thought you were just a dumb hick who only has sex with farm animals,” or verbally castrating Spock for assigning her to the Farragut. Or try to imagine NuUhura singing fun improvised lyrics like Uhura Prime in Charlie X.
Also, NuUhura would have no problem speaking Klingon in TUC, but probably couldn’t rebuild the comm system in Who Mourns for Adonis.
Nichols could totally pull off both lines.
Whether Nichols could pull it off isn't the question, whether it's in character is.
Uhura Prime is capable of being a badass if she has to be, as we see in Mirror and TSFS. However, it's not a part of her natural personality. She's usually in a cheerful mood and almost never shows anger absent extreme provocation (like being sexually assaulted on Triskelion). She shows tenderness and vulnerability more than toughness.
By contrast, badass seems to be the default mode for NuUhura. She's capable of showing tenderness in extraordinary situations, as we see with Spock after the destruction of Vulcan and death of Amanda. However, tenderness, let alone vulnerability, is not something she lets show under normal circumstances. She will never utter the words, "Captain, I'm frightened."