Here's my thoughts on the types as whole in the current metagame, feel free to disagree if you wish...
Normal: the best offensive type but defensively it's rather average because it lacks resistances besides fighting.
Fire: pretty mediocre offensively and really bad defensively, though it does resist Stealth Rock so a few pokemon with a better secondary type like Volcarona can benefit from it.
Water: not as bad as I thought. It has two useful resistances (especially Grass) and decent neutral coverage. Being able to beat grass types is a big plus.
Grass: a metagame-defining type, which makes grass, water, electric and ground moves more common than usual, so defensively it isn't as good as it should be. Offensively it one of the best types though.
Electric: Decent offensively, but only 1 resistance and 3 weaknesses, though only 2 of them really matter (lol Steel).
Ice: the best defensive type and surprisingly enough it's also pretty good offensively because it's the only type SE against ice, making ice attacks a necessity for most teams.
Psychic: it's very close to Gen 1 Psychic, having excellent neutral coverage and relatively uncommon weaknesses.
Ground: thanks to its advantage against grass, it's decent both offensively and defensively, though the SR weakness hurts.
Rock: the second or third worst defensive type because of its Normal weakness, and offensively it isn't that good since it's resisted by common ice, bug and flying types.
Flying: a pretty bad type. It's weak to ground, grass and bug and it's SE only against steel, electric and rock, 3 uncommon and defensively poor types.
Bug: very similiar to grass, though slightly worse offensively in exchange for a better defensive type. Overall one of the top 5 types.
Ghost: it has an awful normal weakness, but it's strong offensively and it's notable for being the only type SE against normal. Unfortunately Shadow Ball and Shadow Claw don't quite cut it against defensive behemoths like Chansey and Snorlax. Overall it's pretty mediocre.
Dark: an average type much like in singles, except its relationship with Psychic and Fighting types are reversed. Overall a decent type.
Steel: to call it "the ice type of inverse battles" is an insult to ice types. Not only is it utterly atrocious defensively, but it's terrible offensively as well. Avoid steel types unless you have a very good reason to use them. At least they can make good use of Weakness Policy...
Poison: the true ice type of inverse battles. Excellent offensively, though resisted by an important type (Grass), below average defensively, though resistant to another important type (Psychic).
Fighting: actually pretty good both offensively and defensively besides the SR weakness. Being the only type that truly counters Psychic types is also a plus.
Dragon: one of the best offensive types, resisted only by itself. Defensively it's rather average and the grass weakness is especially troublesome. Overall a solid type.
Fairy: pretty bad. It's SE against uncommon types and resisted by the common dragons. Its common weaknesses do it no favors either. It does have decent neutral coverage though.
I'll give my take on it too. I'm only good at the gimmicky kind of metagames. :)
Normal is a great type, as it is only weak to Ghost, and can hit Ghosts and Rock types super-effective now. Don't expect to plow through everything with Boomburst and Return because of Avalugg and Chansey (though Choice Band Diggersby can be a huge pain for Avalugg if it catches it on the switch, even more so with Facade). Don't use Slaking, kiddies! Avalugg will block you every time.
Fire isn't the best, with weaknesses to Grass, Bug, and other Fire types.
Water is decent for taking Grass moves, but watch out for all the Ice moves flying around.
Grass is a powerful defensive type, especially in the form of Tangrowth. Offensively, Skymin can fling around Seed Flares, and Chansey hates Leech Seed.
Electric still can't be paralyzed, which is worth considering as Thunder Wave sees some use. The loss of effectiveness against Water and Flying hurts it somewhat, but you may want to carry it for the odd Grass types such as Tangrowth or Breloom. Ground types are common enough (Diggersby, Flygon, even Groudon) that it can be good for taking them out.
Ice is the best type, at least defensively. Avalugg is the physical Blissey standard OU could only dream of, and it even gets Rapid Spin. The only physical Pokemon it fears are Shell Smash Cloyster and Black Kyurem with Ice Beam. Articuno is also a beast with Roost and Heal Bell. You need some Ice attacks to take out Avalugg at least. Mono Ice is no longer a gimmick, kiddies!
Psychic reclaims much of its Gen 1 glory, only being resisted by the uncommon Fighting and the more common Poison (see Scolipede, Gengar). You may want to carry Psychic attacks to take out stuff like Malamar and Mega Alakazam.
Ground is good for taking out Flying types now, and I've taken quite a few Grass attacks with Diggersby.
Rock has a Normal weakness, true, but Tyranitar can eat Water, Ice, and Grass attacks and laugh in Kyogre's face. I wouldn't count it out.
Flying now resists Electric, but trades it for stuff like Grass and Bug weaknesses. Still, beware of Articuno.
Bug is another good typing here. And you thought U-Turn was just for switching. . .
Ghost gets new weaknesses, but now it becomes worth considering to take out the Normal types running around like Diggersby, Chansey, Cincinno, and Snorlax.
Dark is somewhat underwhelming here, at least in my experience. Of course, this tier allows Darkrai. . .
Steel is now a crummy typing. Why do so many people think they can take Aegislash and use the Kings Shield and Swords Dance set like in OU? Genesect is good, but more for Bug than Steel.
Poison can take out Ground types now, and I've had Diggersby taken down by Sludge Bombs before. Psychic resistance is always good.
I hardly see Fighting types, so I can't say much about them here.
Dragon is only resisted by itself now, so beware the Black Kyurem and Rayquaza. However, its defenses leave much to be desired with Water, Electric, and Grass weaknesses.
I hardly see Fairies here. Having a Dragon weakness doesn't do it any favors.
