I really like the Engineer update. It, more than any other class update*, flat out increases the power of the class. The ability to move buildings is a huge bonus, and has no drawback whatsoever. More than a few times I've seen an Engineer plonk down a level 3 sentry near an enemy spawn, thereby winning the game. To be fair, this doesn't work most times, but occasionally it does. There's no way an Engineer could have reasonably done this before the update.
The Frontier Justice is balanced, if you ask me. Having only three shotgun shells is a pretty big drawback. The guaranteed crits are cool, but the Engineer is so fragile that you can't go on a roaring rampage of revenge. Revenge Crits don't survive after your death, so you'll rarely actually use the 14 crits you earned on that epic sentry.
It seems that most people agree that the Wrangler is basically a buff. The pistol is pretty crummy in most situations, and the Wrangler is HUGE in adding versatility to the Engineer. Now you can put Sentries in spots that would make no sense without the Wrangler. Basically, sniper decks are completely legit for sentries with the Wrangler. It seems to me that Wrangler sniping is de facto balanced, since it has essentially the same power level as a good sniper in the same spot, and has the same weakness to enemy spies and snipers that a sniper would have. A long range Wrangler is extremely vulnerable to snipers in particular.
I want to experiment with using the Wrangler while being physically distant from the actual Sentry. There's nothing requiring you to stick with the Sentry once it's built. Seems like you could use the shotgun to penetrate around corners, then back out into the open and wrangle people if they tried to pursue.
The Gunslinger is a lot of fun. Dropping mini sentries is sweet, and the extra 25 HP means you can get into the thick of it a little more. It requires a different mentality to use the mini sentries properly: you have to use them to add to the force around you, not as a force of its own. In other words, you don't use a mini sentry to defend a point, you run ahead with your team and drop the sentry in the back of the fight, hoping to get the extra damage in to push them back or finish of one or two people. The position of mini sentries is less important than the timing of mini sentries: if you can get one up while the enemy is still engaging your allies, the enemy has to deal with the sentry, your allies, and your shotgun.
I love carrying the mini sentry with me. When you're redeploying it, it goes up so fast, the enemy has essentially no time to react before it's shooting. I'll build the sentry around a corner, pick it up and drop it so it peeks around the corner to benefit from the faster build time.
The other thing about the Gunslinger is that you shouldn't protect or reload** mini sentries, so you're free to wander away from them. The true Gunslinger remembers to instantly put up a new mini sentry the instant the first one goes down, even if it's in a bad position, since you can move them now.
The big question now is, "will moving level 3 Sentries or the Wrangler be nerfed?" It's clear Valve wanted this to be an update that increased the power of the Engie, but is this a little too powerful? The way that level 3 sentries re-assemble can make it very difficult to destroy them; I've put up a level 3 under fire from a Heavy in medium-close range, and I ended up winning the fight. That doesn't seem right.
PS. The Southern Hospitality is almost purely better than the wrench. Who cares about a vulnerability to fire as an Engineer?
*Except maybe the Backburner, which was fittingly nerfed.
**Fully reloading a mini sentry costs about 100 metal, you may as well just build another.