The A3340 had multiple record heads, so you could play back what you had recorded and mix that in with new material on the same track (Sound-on-Sound). Or, you could record on a different track (Sound-with-Sound). The 12-inch reels and wide, thick tape allowed for a high signal to noise ratio and high tape saturation value so that you could record with much less noise and a much hotter signal than with cassette recorders (which were pretty new at the time).
Over the years, cassette tape coatings got better and better, so that the audio values were closer to that of the open-reel recorder. However, the open-reel machines also benefited from the new tape formulations.
In the end, I think that it was just economics that made the open-reel recorders so rare today. The machines and tapes were very expensive.
I suspect that your A7300 is a more-expensive model than the A3340 that I used, and that it would have more features. I would suggest that you get the recorder checked for tape speed and drag and head alignment. Open-reel tape systems required a lot of maintenance to keep them running - if you record now without ensuring that the tape transport is in good condition, you might come back later and find that your old tapes no longer sound right.
