Watched the first 7 min so far and I see what you mean. It feels like I'm really watching TOS! The guy playing Kirk pretty nails it. I find Kirk and Spock's voices a bit awkward though.
And since the debate has already begun... I'm a fan of TNG as well. I think it was the better show from a story telling perspective. TOS may have been historically more important but TNG influenced just as many lives (or more). As a successor to a series TNG pretty much knocked it out of the park. DS9 I liked a lot as well. Voyager and Enterprise not so much.
It's definitely tough wrapping your head around new voices, when you've had more than 40 years to get used to the originals. From the acting standpoint, though, I would say that the main cast hits the high points of their roles quite well. Chris Doohan, son of James Doohan, is sometimes creepy good when it comes to stepping into his father's shoes. Grant Imahara is occasionally successful at getting George Takei's voice cadence down but should probably just stick to playing the character, like Habercorn and Huber do with Spock and McCoy, rather than trying to do an impression.
I think that my main sticking point, with the shows that came after, was that they needed a season or more to catch their stride. TOS just hit the ground running and never looked back. To me the first seasons of NG and DS9 were complete throw aways with wooden characters, and rough plots. In the case of DS9 it was apparently because all of the good writers were still with NG and when production on it shut down, DS9 improved noticeably. If I was the captain in Voyager I'd have spaced the entire mutinous crew, before season 1 was over, and would never have gotten to the Borgwatch seasons. Enterprise was a squandered opportunity. They could have done the founding of the Federation, in fact they started to do that very thing just before being cancelled, but instead went for that ridiculous "temporal cold war" storyline.
"Star Trek: Axanar" looks like it might pick up some of what Enterprise should have done. I'm expecting my DVD soon.
https://www.kickstarter.com/projects/194429923/star-trek-axanar
Here's their intro video "Prelude to Axanar":
[video=youtube;1W1_8IV8uhA]https://www.youtube.com/watch?v=1W1_8IV8uhA[/video]