Since online-go is my first ever Go server when I picked up Go this April, Iāve always been a quiet loyal member to this website. The fact that I play here most probably gives away my vote.
However, in my double digit kyu days I ventured forth into the territories of KGS, IGS, FoxWeiqi and Tygem. Hereās a then-double-digit kyuās viewpoint on the servers:
KGS:
Iām a perfectionist when it comes to design, and I could not tolerate the 1990 style KGS GUI littered with rounded buttons and muted grey colours. To me it looked old, outdated and unappealing.
While that was discouraging, I had a lot of troubles finding a game (as mentioned by previous posts). I was 15 kyu (OGS) when I got on to KGS, there were hardly any fellow DDKs there. Mostly all single digit kyus. It would seem like other 12 - 15 kyus refuse my game request even though weāre ranked similarly (and I made sure I wasnāt given handicaps or more komi), not sure if they just hate my username or somethingā¦
In terms of play style, at least in my DDK viewpoint, it felt like 80-year-old grandpaās go: itās very framework v framework and territorial. I enjoy fights and mess on the board.
Unable to find many games, I grind my way up to 12 kyu on a 12k bot. Only then did I mange to find a game. It took way longer than here, and I didnāt want to go through the trouble again.
One thing I do like about KGS, is how accessible the teaching games are. I played a few games with dan level players, and they pointed out my mistakes and got me better at the game. There are separate rooms and members are very active there. The fact that thereās a live chat that is easily accessible is very handy. Maybe on OGS the public chat should be made more accessible (rather than a link on the top bar).
IGS
Frustrated at how long it took to find a game, I quickly decided to seek some other servers. I forgot where I heard of IGS, maybe on senseiās library. Nevertheless, itās more of a Japanese server. GoPanda2 client looked stunning, and the go board looked marvellous. I played about 100 games on there just because I was hooked to how aesthetically appealing the client was (I know, Iām a pushover when it comes to that). At first I thought the players said āHi!ā every game by themselves, and I was pleasantly surprised at how friendly they were⦠Until i realised it was an automated message, then I doubted how necessary that was to implement.
Playing there has improved my strengths, going up to around 13k. I do have to say, the DDK there have a very annoying play style. Lower DDK prefer to lean on your stones and build borders all the time. These games are boring because thereās 0 action. Itās all outline vs outline.
Then there are those who, at endgame, will not stop playing stones in your territory in hopes that you blunder and they can get something out of it. Trust me, theyāll reduce your large space that even a dan level player would know itās impossible to live in, into nothing but single eye spaces, leaving a trail of dead stones in their wake. They refuse to pass moves and are extremely persistent with hopeless things. Honestly, I really want them to stop wasting time and get on with it. On a bad day, this can drive me insane.
The other thing about this server is that the ranking process is too slow, time setting is not flexible enough (often having very long games due to the canadian time setting everyone uses). The slow ranking process means that the player skills are very inconsistent with their rank. I played against 12 kyus who demolishes me, but I also played against 8-9 kyus, winning with ease.
Ok, in terms of real player style here: the DDKs will just try and surround and kill. Your knights approach to a 4,4 will almost always be answered by a kick. Sometimes going as far as removing your base as soon as you extend. Players hardly resign, at least not the ones I played against, and theyāll do anything to win. Good fighting spirit.
FoxWq / Tygem
It seems like it is a trend with Asian servers that the players are generally much more aggressive (compared to, say, KGS). In my 12 / 10 k days I went to these servers for a change and got wrecked by a 16 kyu because I was horrible at fighting. I definitely recommend playing a lot on Tygem, because fighting is an important skill. Playing a lot here has allowed me to differentiate what is a reasonable fight and what is not a reasonable fight to start.
I specially enjoyed the poor english translations on these clients. Partly because Iām Chinese and I know very well why the english is translated poorly: sometimes a phrase in Chinese is said differently than how it is expressed in English, and a ābrute force literal translationā just doesnāt work!
There are some very bad mannered users here, though. Some wants to start counting at move 20. Some refusing to count when all dame has been occupied. Some straight-up leaves when they know theyāre about to lose. Then there are those who seem to have connection issues, and the timer freezes on them. A game I had lasted for an hour because that person was having connection issues. For each move I play Iād wait at least 2 minutes for his move. But then the timer says I used more time than him⦠Oh yes, and I love the sandbaggers. This 18 kyu with 1k wins and 7k losses desscimated me across the board, only to resign and give me the win. Gosh what a weird feeling.
OGS
Ah, back home. I love OGS because how easily accessible it is: no downloads, just a URL and away you go. That is not to say it doesnāt need more work, but then again, thatās just how servers go. The players here seem to be a bar stronger than what the other servers indicate. A 10k here plays just as well as some 8k on other servers. Thereās a nice variety of play style: some aggressive, some too passive, some defensive, some territorial, some influential. I also enjoy the rank system, one because itās fast to grow and drop, allowing one to assess their true strength in a few games (whereas iām still a 11k+ on Pandanet because I couldnāt be bothered playing that many games to rank up and the play style there gives me more headache than I can handle). The other one, too, since it is a bar above the ranks of other servers, having your goal set at 1 dan means youāre probably a 2 dan when youāre 1d on OGS 
I definitely recommend on playing all of these servers. The servers, just like people, have quite a bit of diversity to them, and to be able to adapt to change is also part of becoming a truly skilled Go player.