A saved person now has the ability to not sin. Will they always exercise that ability? No, just read about Paul's struggles in Romans and John's admonitions about saying we are without sin in First John.
OK, so this new nature is one where we are free to do good or to sin. Is that a fair restatement?
In the old nature, there was nothing possible except to sin. Is that also right? You said "a saved person now has the ability to not sin." From this I conclude that before being saved they did not have this ability. Therefore it was all sin.
OK. So what were we talking about? Oh, right. Does having the ability to sin or not sin, the freedom to choose, make one greater than God, who is not in his nature able to sin?
SD