It's going to end up rather subjective to attempt an answer of this, I think. Some words in modern Norwegian sound like old fashioned Swedish to Swedes and vice versa. "Spørga" for example has the direct Swedish equivalent "spörja", meaning exactly the same thing, except this is archaic Swedish that isn't used any longer (replaced by "fråga"), while modern Danish/Norwegian use it.

I found lots of interesting reading on the subject at Wikipedia: https://en.wikipedia.org/wiki/North_Germanic_languages. There seem to be no historical claims that any of the languages are somehow more "progressive"/"conservative" than the others.

I agree with the existing comments, partly because languages are complex systems and it's quite subjective to choose between syntax, morphology, phonology, lexicon, and so on. Further complicating dimensions of comparison are media (spoken/written), genres, styles, registers as those can greatly differ in conservativity, too. However, if you'd be interested in a feeble, lexicon oriented attempt at an answer, let me know.

@Jirka Hanika There is no answer thus far, so please give it a shot.