Admittedly…, but: 〜ものの

〜ものの acknowledges a first fact (“admittedly…”) then announces that the expected follow-up didn't happen: “although…, even though…”. You've taken a step, but it goes no further; a hint of disappointment or incompleteness often comes with it. Written or careful spoken register. At the start of a sentence, とはいうものの means “that said, even so”.

• 免許は取ったものの、まだ一度も運転したことがない。めんきょはとったものの、まだいちどもうんてんしたことがない。I did get my driving licence, but I've never actually driven.
• 日本語を三年勉強したものの、敬語はまだ苦手だ。にほんごをさんねんべんきょうしたものの、けいごはまだにがてだ。Even though I've studied Japanese for three years, I still struggle with keigo.
• 名古屋城まで行ったものの、休館日で中に入れなかった。なごやじょうまでいったものの、きゅうかんびでなかにはいれなかった。I went all the way to Nagoya Castle, but it was closed that day and I couldn't get in.

〜ものの starts by admitting a fact: “yes, I got my licence”, “yes, I studied for three years”. Then the sentence turns round: what you could have expected from that fact didn't happen. It's the “admittedly…, but” of a story or a confession.

The typical nuance is one of incompleteness or mild disappointment: you took the first step, and stopped there. The tone stays calm, without anger.

• 「やります」と言ったものの、あまり自信はない。「やります」といったものの、あまりじしんはない。I said “I'll do it”, but I'm not all that confident.

ものの follows a plain form, very often in the past. With a な-adjective: な or である; with a noun: である. とはいうものの (“even so”) is used after a noun or at the start of a sentence to qualify what came before.

• この部屋は駅から近くて便利なものの、少しうるさい。このへやはえきからちかくてべんりなものの、すこしうるさい。This flat is handy, close to the station, but a bit noisy.
• 彼女は日本人であるものの、海外育ちで漢字は苦手だ。かのじょはにほんじんであるものの、かいがいそだちでかんじはにがてだ。Although she's Japanese, she grew up abroad and kanji aren't her strong point.
• 春とはいうものの、まだ寒い日が続いている。はるとはいうものの、まださむいひがつづいている。It may be spring, but the cold days keep coming.

The second part is an observation: what happened, or what didn't. Never a wish, an invitation or an order. For “it's expensive, but let's buy it”, you go back to けれど or が.

• 高いけれど、買おう。たかいけれど、かおう。It's expensive, but let's buy it anyway.
• 頭では分かっているものの、なかなか実行できない。あたまではわかっているものの、なかなかじっこうできない。I know it in theory, but I find it hard to put into practice.

けれども (N4) contrasts two facts neutrally and accepts any follow-up. のに expresses strong emotion, reproach or frustration, mainly in speech. ながらも, written, combines two states of the same subject (“while being”). ものの is more composed: it admits a fact and notes it didn't lead where you thought.

• あんなに練習したのに、負けてしまった！あんなにれんしゅうしたのに、まけてしまった！We trained so hard, and we lost!
• 狭いながらも、楽しい我が家だ。せまいながらも、たのしいわがやだ。It may be small, but it's our happy home.