I hope #2 is the Tascam, because it sounds like it has more depth. #1 sounds like it has a hashy sheen laying on top of the sound. #2 sounds like the hashy sheen has been removed and you can walk right into the gym. Listen to the "T" in "light". In #2, the T sounds crisp. In #1, it sounds slightly fuzzy.
The other advantage to an external recorder is the bit rate. Cameras record audio at 16bit, recorders at 24bit. That means you can record to the Tascam (or Zoom) with a conservative input level without using the limiter. In 16bit, you'd need to get as much level as possible before clipping, and you'd need to use the limiter to avoid clipping.
If you're in an environment with unpredictable sound levels, you can use the other two tracks on a 4 channel recorder for a safety recording with the input levels 12 db lower. That way, if the regular recording clips, you can switch to the safety recording to get clean audio.
On your recording, if you wanted "better" sound, you'd need to set up the recorder closer to the singers, which isn't always possible in that scenario. The room sound in your recording is not the fault of the recorder, it's the fault of the room.