I liked the granularity of 3ed's skill system but it was needlessly complex. It added significant time to character creation and leveling up for little gain at the table. And it got messy when multiclassing.
As mentioned previously, 5E's skill system is an improvement over 3ed in every way. However, like many systems in 5E, goes just a bit too far towards simplification. I'd like to see more than just trained & untrained as it makes characters feel very similar in what they can do.
This recent thread (
5E - Using different skills in 5e) was a good discussion on variant skill ideas.
I'll agree that 5e's skill system is
different in pretty much every way. "Improvement" is a matter of opinion. I prefer the 3.* system because of the ability to focus training in particular areas as the character's level advances. That's slightly distinct from the "granularity" aspect, in that it's addressing adaptability.
In a system where skill concentrations are selected at character creation time and then adjusted sporadically (if at all), the player needs a certain amount of precognition, or be a really good guesser, with regards to making a good skill fit.
Progressive systems, like 3e, allow a character to learn and grow based on experience (not EXP but the things they've faced), and to change course on the fly.
Now that assesment is based on my 4e experience, and my slightly dated 5e experience, where the opportunities to train in skills was limited, and used Feats. If I'm off target, I apologize.
To illustrate the extreme case, consider the Ranger type who has skills trained in hunting/tracking/wilderness survival. You know, the usual Ranger stuff. Now you, the player, find that the campaign will focus almost exclusively on seafaring and swashbuckling, and travel to (large) exotic ports. As in, little or no wilderness.
Said Ranger is going to be a fish out of water (or whatever the opposite of that is) for the bulk of the campaign, and behind the curve for all of it. Essentially useless when it comes to applicable skills.
In a progressive system (one that goes beyond trained/untrained), the character can adjust to the unexpected campaign direction, and become useful again in relatively short order.
So in that sense, the trained/untrained approach is distinctly not an improvement on any level.
At least, in my experience and opinion.