I've played a few games with Protective leaders, and as far as I'm concerned, the jury's still out.
The most obvious trait to compare with Protective is Aggressive, of course. It would also be valid to compare Protective to Charismatic and Imperialistic, but let me stick to the Aggressive comparison for now, since it is the most "apples to apples" comparison. So, what are we comparing?
- Drill + City Garrison (Gunpowder) vs Combat (Gunpowder)
- Drill + City Garrison (Archery) vs Combat (Melee)
- Cheap Walls and Castles vs Cheap Barracks
OK. For point #1, we have two situational promotions for Protective, versus a single all-purpose promotion for Aggressive. City Garrison has obvious uses, while generally speaking, Combat I is more useful than Drill I. Drill offers advantages over Combat I when fighting with a significant strength advantage (either due to attacking weaker units, or defending with terrain/city bonuses), and when defending against Siege. In most other cases, Combat I has the edge. Due to the BTS changes to the promotion tree, Drill I allows access to most of the "specialty promotions" that originally were only open to Combat I, so I'll ignore that line of argument.
The simple question that you have to ask is: how often do my units fight battles where their advantages come into play? That seems to be the core question. In offensive city assaults, I'd say that Combat I is more useful than Drill I, but not by a lot. It all comes down to those few battles between the initial siege sacrifice, and the final >99% "clean-up" actions. Combat gives a better success rate in that window, while Drill units have a better chance of requiring zero healing after that window.
Also note that there's nothing preventing you from giving Combat upgrades to your Protective gunpowder units. Combat II vs Combat I + Drill I is not a lot of difference, though of course the relative STR of the defending unit matters a lot here.
Another question is whether or not you ever fight battles where you are
defending against an AI stack, especially while in a fortress or city. In these situations, Protective is FAR more valuable than Aggressive. Hopefully, this is obvious. Bhuric's argument stems from the assertion that these types of battles are rare, while Protective proponents argue that it's quite possible to manipulate the AI into these types of battles. Fair enough. I'm not really skilled enough to compel the AI into suiciding against my cities, though I'd be happy to see some demonstrations of this strategy.
When Gunpowder finally comes around, I'm leaning towards Protective, though only a little. The ability to both attack AND defend with your bonus promotions makes up for the small difference between Drill I and Combat I.
Point #2: Here, the differences between Aggressive and Protective are more pronounced, because you have to build different types of units to exploit the bonus. If you never build Archery units, then obviously Aggressive is the more valuable trait. If all you want is barbarian defense, then both Aggressive and Protective gives you adequate units for this task.
However, if you spawn without metal, than Aggressive is positively
useless, while Protective may very well save your hide while you bunker down and tech to Catapults.
So, in the pre-Gunpowder era, I'd say that Protective is more flexible, but Aggressive gets the edge when you have metal and a close neighbor.
Point #3: Cheap Barracks vs Cheap Walls/Castles. Again, we're talking about a single strong bonus vs two weak bonuses. Barracks is a good, solid building, but if you concentrate on city specialization in the early game, you will probably not need more than 1 or 2 of these. Walls are pretty weak, but they do occasionally come in handy if you're the victim of a sneak attack and need to hold out a few extra turns while you consolidate your army to the front. And, as Wodan has pointed out, walls increase your power rating and help prevent getting attacked in the first place.
Both Castles and Barracks have uses during the mid game (around where Nationalism comes online), and there are good reasons to spam either: Barracks to boost happiness and draft-XP with Nationalism, and Castles to boost trade and espionage. Due to the higher cost of Castles, you are probably going to get more

-savings from castle spam than barracks spam, but to properly exploit Castles, you need to beeline Engineering, which may not be the optimal tech path for your strategy.
So, here, Aggressive is the more flexible trait, since the cheap barracks don't compel you down any particular technology path.
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In summary, I don't know that I really favor one trait over the other, when comparing Aggressive to Protective.
In my games, for example, I like to beeline Archery and build a handful of archers before building my first Settler. Why? Because I don't like gambling on Copper and having to restart my game whenever I don't get it (raging barbarians are a harsh teacher). This strategy blends really well with the Protective trait.
However, I also like to favor aggressive play when my position allows for it. The Aggressive trait comes in very handy here.
I think, when it comes down to it, it really depends on your starting position. If you end up with metal, then Aggressive is the stronger trait. If you end up without, then Protective is the stronger trait. Incidentally, if you end up with Horses but not metal, then I would argue that Charismatic is stronger than either.
Your Mileage May Vary.