I thought Peck did a pretty good job as Spock on the last episode. But it looks like Spock is going to mature very quickly between DSC and TOS. Peck never plays him as truly dispassionate. There's always this underlying level of snark underneath how he behaves. Nimoy did that too, just not constantly.
In fairness, people usually change quite a bit over a 10 year period. Spock, as played by Nimoy, even evolved over time. Of course, he had life-death-life to help with some of that!