One thing my last DM did that helped at high levels (also low levels, but especially high) was to split solos into, effectively, three monsters. So a dragon might become the head, the body, and the tail; while a demon might be head, body, and arms, depending on the powers. He would divide the solo's actions up and give each piece hitpoints so that two of the pieces were equivalent to an elite monster and the third was equivalent to a standard monster. Each piece gets its own initiative and set of standard/move/minor actions, and players target pieces separately (so, for example, an assassin could shroud the head, but wouldn't get shroud damage if he then attacked the body).
You would want to adjust the specific mechanics for your own game - we tended to address issues like whether "slowed" affects one piece or the whole creature on the spot and depending on how the creature was split up - but if your aim is to reduce complexity, it would be worth figuring out satisfactory answers to common effects up front. Then once play starts you already know the answer.
It ends up being significantly simpler for the DM since you have the strength and threat of three monsters, but the abilities and powers of only one to keep track of. It also requires fewer additional monsters/terrain/whatever to build out the encounter, again reducing the complexity of any given combat. You also get the advantage that a combat against a solo becomes much more interesting, because you've got three parts of the monster moving and acting independently (preventing the solo from being pinned down and focus-fired), which again increases the fun without increasing complexity.
The Real Problems Did Not Get Fixed
But let's talk about these individually.
Multiple Attribute Dependancy
Also known as MAD, this has plagued the poor Monk for ages. Monks need Strength for accuracy and damage, Dexterity and Wisdom for their armor class and two saving throws, Constitution for hit points (to be fair, all characters want this) and their last saving throw, Intelligence for skill points and Charisma to make use of their short list of social skills. This is not a good thing, because there's only so many high or even mid ability score numbers to go around. Pathfinder seemed like it was going to help this when it improved the skill system, consolidating many skills and relieving the reliance on Intelligence, but then it turned right back around and made boosting your ability scores with items more expensive, actually worsening this particular issue.
Anti-Synergistic Class Features
This just straight-up didn't change. Many of the Monk's class features are mutually exclusive with other features, with the use of feats, with the use of skills, or some delightfully awful combination of all three. Additionally, Monk still has problems making use of combat maneuvers (due both to low numbers and the increasing Size rating of stock enemies) and the feats relating to those maneuvers got weaker, cutting off a theoretical avenue of contribution.
More Melee, More Problems
Traditional problems with "mundane" or "melee" classes like Monk, but also like Fighter or Barbarian, were not solved by Pathfinder. They still have problems with enemies of all kinds that fly, burrow, teleport, cast spells, use "lockdown" effects like paralysis or poison, and utilize battlefield control (spiderwebs, choking fogs, etc) among other things. Like all melee classes, the Monk is forced to funnel enormous amounts of cash into meeting the increasing demand for complexity as levels and challenge ratings climb ever-higher. Unlike other melee classes, Monks cannot shore up their "primary" role, because...
Monks have no specialization
And, unlike Rogues or Bards, Monks cannot be made into competent generalists because of the aforementioned anti-synergy and low numbers, forcing them to pour resource after resource into badly mimicking another class's role.
On Monk's defence: the Archetype system
Pathfinder did introduce the Archetype system, a refinement on the idea of Alternate Class Features from 3.5e. Some Monk archetypes, such as Zen Archer and Hungry Ghost, work to alleviate some of these issues. Combinations of archetypes, done intelligently, may make for a playable character whose class still reads 'Monk'. Whether or not such a thing is worth the effort is not easily decided, but the options are available.
Monk changes very often
With that in mind, a word to the wise - Pathfinder gets errata often, and Monk has been the subject of many heated debates and quick rules changes, such as the brief-lived errata to Flurry of Blows. This does not have to affect your table, but if you're participating in a sanctioned table (like in Pathfinder Society) or if your group cares about such things your Monk may find the rules shifting out rapidly from underneath him. Caveat emptor.
Best Answer
Here's One Player/DM's Experience
For the DM, 5e is much, much easier to manage and the combat flows much faster than 3.5e. High-powered monsters have much simpler mechanics and strategies, and yet they still "feel" powerful and interesting - thanks largely to the "legendary actions". Thanks to the simple advantage/disadvantage mechanic there are fewer rulings to make and its much easier to answer the fundamental question of combat: Did I hit? Hit points and damage levels are generally well-balanced, so a 15th level combat doesn't take all that much longer than a 3rd level combat with a similar number of figures. That said, high-level combat in other systems can be brutally short due to save-or-die mechanics, which are nearly absent in 5e.
For the player, preparation for spellcasters takes roughly as much time as in other editions, depending on the particular class. But I find that there is one huge difference, and that is that in 5e getting the preparation right is much less important. A player doesn't have to obsess over getting just the right set of spells for their caster to be effective. You can pick up a blank character sheet and draw up a 15th-level wizard in the minutes before the game, pick out spells based on how you like the names, and your character will still, more likely than not, have a successful adventure.
In my experience, the theater-of-the-mind style can work both ways. At times it can slow things down as players pepper the DM with questions. On the flip side, it eliminates fussing over things like how precise can an area-effect spell be figured. Whether it is a plus or minus for you will really depend on your group.