I would say that the constant temperature wold be better than the freeze-thaw cycles. The freezer should be fine.
Many folks prefer to store their seeds in paper envelopes rather than in plastic due to condensation. When you are saving seeds, moisture is the enemy.
You may put all of your envelopes into an air-tight container and put some corn-starch or silica gel packets in with them to absorb and ambient moisture.
You may also find some good info at [url=https://www.seedsave.org/issi/issi.html]International Seed Saving Institute's Website[/url] too.
Hope this helps.