Interesting. Are you watching the remastered or original effects?
I watched TOS in my childhood, which means late 80's-mid 90's, and I was absolutely enthralled by it. At that point the episodes were 25-30 years old, not exactly brand new.
The only thing that ever seemed dated to me were the women's hairstyles. Maybe now for the latest generation (who grew up with a real communicator and tricorder in their pocket in the form of an Iphone), perhaps TOS feels dated to someone of that era who'd never seen it before.
As for the pacing relative to Berman-era stuff, I doubt there'd be a single episode of TOS that is slower paced than Star Trek : Nemesis, a film that was made in, what, 2000-ish? A group of us re-watched that movie recently, and we all felt like time was going backwards...it was THAT slow.
Anyway, I hope you will watch Seasons 1 and 2 of TOS, and give us your impressions. Season 3 may be a bit hard to sit through, the action/stunts quotient was severely limited in the last year of the show.