Part of the problem I think was the increase in technobabble over TOS.  If your actors are struggling to remember the name of the whatsits this week for thirty solid takes you end up taking the 31st where they actually get the name and the line right.  If you look on the youtubes you'll find some excruciating TNG outtakes where it's the invented tech words that trip them up every time.   Add that on top of the grind of shooting a show that airs weekly.

The other half of the equation is direction.  Even the best, most experienced actors can sound wooden with poor direction.  The early seasons suffer more from this I think due the production team playing it straight and safe with the direction and partly due to the entire team struggling to find their voice.  I mentioned in another thread that TNG had an usually long period of 'pilot-itis', nearly two years and almost forty episodes before it really started to gel.

Its hard for actors to really embody characters when those characters are written in a wildly inconsistent way, also.  I mean, Picard for example is a wild throwing together of seemingly random character attributes.  He's a Frenchman with a British accent who loves British tea.  He also randomly loves early twentieth century detective novels, archaeology, and he either hates children or regrets never having them depending on the episode/movie.  He loves his women prim and proper...or has escapades on Risa depending on the episode.

Data uses or can't use contractions, does or doesn't understand humor, etc. depending on the episode.

Geordi was constantly speaking nonsense technobabble and had no character beyond being brilliant, and lousy with women.

Riker, Troi, etc. were all over the map.  Crusher had no real personality written for her character.

Characters just did and said whatever the plot required on that show.  It was plot driven rather than character driven.  DS9, at least in the later seasons, was just the opposite, which is why I liked it more.  TOS was pretty much a perfect balance between the two.  There was a strong premise to each episode, and then the action revolved around the characters' interactions flowing from that premise. 

***

As Netflix has every STAR TREK series on, I thought I'd watch a TOS episode earlier tonight. And then a TOS one.

I opted for "Who Mourns For Adonais?" and "The Big Goodbye".

I have to agree with what Mr Byrne said. Shatner and others did indeed sink into the roles, whether it was discussing routine Enterprise issues or Kirk discussing gods and Greek culture; "The Big Goodbye" on the other hand, whilst entertaining, did feel very much like actors reading lines. 

So I guess I agree.