I am, of course, obligated to tell you about every online mahjong client I experiment with, even though Tenhou is of such quality that you really need nothing else.
The current experiment is Mahjong Hime, a client that opened just a few weeks ago. It is nearly the same game as the Japanese Momoiro Taisen Pairon (Peach-Colored Wars Pairon). A title like that could only belong to a moe game, and so it is here. The game is mahjong, but the otaku hook is cute girl characters played by famous Japanese voice actresses.
Janryumon has been going this route as well: charging the player to use the voices of famous Japanese VAs, items to make your player character look like one of the schoolgirls from Saki. Pairon just brings otaku interest to the fore, as the player chooses a moe avatar (starting out with a catgirl) and pays game currency or cash to get new characters.
Mahjong Hime is just an English-localized version of this, with Taiwanese and Singaporean styles (both are kind of bonkers rulesets) added as a nice extra touch.
Unfortunately, the English localization is only really halfway: vital info like the scoring screens and yaku are completely untranslated and left as a mystery to the player who doesn't already understand them. Nobody's going to learn how to play using this thing, that's for sure.
Since it's an online game, you're amassing currency to unlock things for the character: you either put game money into unlocking voice clips (which will make her very noticeably chattier) or risque illustrations that don't actually have much to do with anything. The typical "grind faster!" and gacha money traps are, of course, present. Due to the fancier interface, matches (and players) are a little slower here than on Tenhou.
Because it's new, and because it's mahjong, there are very few players online. The players who are there tend to prefer playing against AI bots all by themselves, perhaps because they are more interested in grinding game money than actually playing mahjong. (But playing other people gets you more game money...)
If I start a room, people will come in and expect me to just start a game with two AIs, and get upset and leave because I won't. They don't know why you wouldn't want to play AIs. What's the point of playing online mahjong against a dummy computer? You're online to play against people! But hey, people here seem to like it.
Likewise, I don't think there's a quitting penalty, and I haven't had a 4P match yet where at least one of the players didn't quit before the match was through. Sometimes this is a result of quits, sometimes this is a result of the system's very shaky connectivity.
The competition is very low-level, as in just figuring out the rules of the game, so when I go there I tend to slaughter. If you know what you're doing, you'll probably slaughter too. It's kind of mahjong stress relief compared to the more serious Tenhou.
So Mahjong Hime isn't too great, but it is an Engish MJ client and it does feature moe waifus. If that's what it takes, well then dammit, otaku...
My ID on there is TRIPLE BREAK.