You must like problematic topics because there's at least four threads about this one. And that's just what I'm aware of.
Pros:
- Easy Bookkeeping - you don't have to track a minion's hp, unless he's got temporary hit points. Either he's fine or he's dead / unconscious. Bonus: they do static amounts of damage.
- Heroic Feel - carving through a ton of guys reinforces that the heroes are bad asses. Players (and DMs) respond to that.
- Emphasize Facelessness - Minons are the guys that show up in big numbers. They may or may not be really good at this stuff, but when there are this many of them it doesn't really matter.
- Avoid "Miss" Powers - Nothing makes my evil DM heart brighten like getting to smile when my players tell me "And he takes half damage."
- Both Worse and Better Than "Real" Foes - The math on minions makes them insanely deadly if they get to use their optimal tactics. Four times as many actions will quickly chip through the heroes' resources. On the other hand, taking them out is pretty easy. "If only there weren't so many, we'd have a chance!"
- Heroic Skill - Minions emphasize that your fighters actually do stab people in the heart, cut out throats, sever limbs and crush skulls in combat. They add that gritty touch that makes things feel bloody and brutal.
- Speed Combat Up - Minions are plain faster to run than an equal number of regular foes. Damage resolves faster and they have less to track.
- Epic Duels - Several times, I've been witness to an epic duel between a PC and a minion. The player couldn't hit and the minion couldn't deal enough damage fast enough to kill the PC. However, the PC was tied up for several rounds by a single minion, making the encounter much more difficult for the party.
Cons:
- Anti-Climactic - Having an enemy drop in the first hit, or an entire encounter end in the first action, is usually a let-down. Not always, but sometimes.
- Deadly - Minions are surprisingly deadly. Those epic duels and four times the actions make minions very dangerous.
- Weak Criticals - Minions always do the same damage. Unless you choose to specifically give minions a weapon that does more damage on a critical hit, their damage is unchanged. This is simple and quick but can feel a bit dissatisfying.
- Explanations - The biggest problem with minions is that many DMs find them very, very jarring and difficult to explain. It shouldn't be (these are the guys that novel heroes stab in the heart, throat or head every time they hit them). Honestly, it's no harder than explaining why a 18th level character is nearly indestructible when compared to his 1st level self. But there it is.
Ultimately, the explanation falls to the guy running the game. Are the minions simply more of the same, old foes long beaten, or simply guys that you don't want your players to spend a lot of time worrying about?
From an RP stand point, I use minions just like I use everything else. They are characters with their own lives, personalities and ideas. However, in combat they are probably dog meat, not because they aren't competent but because they don't have that narrative spark that lets them survive ridiculous dangers.
Now, there is no reason you can't replace any and all minions with regular monsters (and you got the DMG ratio correct), but you probably shouldn't.
Now, you don't always have to use the minion version of a monster, especially if it's the first time the heroes encounter one of those and you want it to be memorable. Simply take the minion and give it appropriate hp for it's level and probable role (the new DMG is awesome). Make sure to increase it's XP value.
However, when it's "more of the same" for the heroes, or they fought these guys six levels ago, then you probably want to use minions to emphasize the lack of competition. Minions are a great way for 27th level characters to have to worry about Ogres without being worried; making the Ogres level 25 minions makes them useful in the combat without making them more dangerous than a long-conquered threat should be.