I don't think it is harder to DM 3E. I have played Basic/Expert D&D, I have played 1st Ed. I purchased the one of the first copies sold of 2nd in Albuquerque. (I was in the store when the shipment came in. I watched it come off the truck, I watched the box being opened, etc.

) I have 3.0 and 3.5.
I have been running games for 23 years. I have experienced burnout, I have made my share of bad guesses, I have even run a few good games.
With 3.0, I can allow my players to create unique characters with the modular rules without worrying too much that they will build a character that will completely overshadow other characters on the table. I have much fewer arguements on why an action can/cannot occur based on real world science/logic. The rules are clear enough that there is a strong framework for an agreed upon shared reality.
The framework is strong enough that I can make an arbitrary decision in the middle of a game to provide bonuses or penalties and my players agree (The +2/-2 rule is easy). I can decide that we don't want to look up a particular rule at the moment, assign an arbitrary modifier, tell my players that the rule will stand for the rest of the session and we can look it up before we game again. They don't seem to feel like they are being mistreated and the arguements don't happen very often anymore.
I do not think that 3E encourages combat over RP. In the game that I play in, we had a half dozen combats over the course of the first (RL) year we played. The rest was social situations, exploration and similar non-combat encounters. The group I run can have a half dozen combats in a single session. One group prefers RP, the other prefers combat. I would argue that this is a difference in personalities with some possible modifiers for age. In the group I play in, I am the youngest player (I am 33). In the group I run, I am the second oldest person there.
I have not encountered as much DM vs Players with 3E. Of course, part of that is probably changes that I have undergone through the years.
I would argue that DM burnout has always occurred. The increasing usage of online environments makes it easier for the gaming community to discuss these issues. So, it isn't that more DM burnout happens, it is just reported more often. And we seem to be having a cycle right now that refelcts the release date of 3E rules. Many people looked at the rules, were excited and felt their creative juices working their magic. So, many people started new campaigns around the same time.