Quite honestly, I preferred NBA Jam, myself. I wasn't a fan of Hangtime or Showdown. I can't put my finger on it, but I liked NBA Jam, and had fun playing it. In fact, I liked the Sega Genesis version of NBA Jam over the SNES version.
But when it comes to NBA Jam and Hangtime and Showdown, there was just something about Hangtime and Showdown that really turned me off about the games. I can't place my finger on it, but I just didn't care for either. I always preferred NBA Jam, and played it a lot.
Now, between the SNES and Genesis versions, I liked the Genesis version better. The SNES looked a little crisper, and the button layout was better on the SNES controller. However, the A.I. wasn't as good on the SNES as it was compared to the Genesis version. Also, the Genesis version had more announcer voice acting. He said all of the arcade lines. The SNES version only had half of the lines, and they repeated them alot. So you got a lot more variety in the Genesis version. The SNES you kept hearing the same thing more often. Also, the Genesis had more voice acting in other menus as well, that the SNES version didn't have. And, the music. The Genesis had the arcade music, and had music all throughout the game. Even when playing the game. The SNES had a different tune at the beginning of the game. And it didn't have music playing in all of the parts that the Genesis had. So, for me, the Genesis was the better version. Tho, combining the Genesis version with the SNES controller would of been great.
But yeah, the other games just felt 'weird' to me, for some reason. I can't explain it. I just didn't have fun playing Hangtime or Showdown. I had a blast playing NBA Jam. But I didn't care for Hangtime or Showdown. My brother, on the other hand, loved Hangtime the best. He loved NBA Jam, back when that was the only one. But once Hangtime came out, he 'forgot' all about NBA Jam. So, he played Hangtime and I played Jam.
However, like I said, my vote goes towards NBA Jam, myself.