I haven’t tried the Arctis 1 Wireless yet, as no stores near me have it in stock and I don’t have any kind of working relationship with SteelSeries so I didn’t get a review unit.
Getting an Arctis 1 wireless is a low priority for me right now also, since it’s not a big change from the Arctis 1 aside from the new receiver.
I don’t expect the Arctis 1 wireless to sound any different from the rest of the lineup as SteelSeries is still using the same S1 speaker driver.
The Arctis 1 wireless and Arctis 3 Bluetooth have different connectivity features and I don’t know that they’re directly competing at all.
The connectivity options are the biggest differentiating factor, so you should buy based on the connection choice you need.
If you would benefit from Bluetooth at all, go for the Arctis 3 Bluetooth. Bluetooth is best-suited to music and movies over games, and you’ll need a Bluetooth compatible device.
The Arctis 1 wireless connects specifically through its proprietary wireless USB-C receiver, designed for Nintendo Switch, Android Phones, PC, and PS4. It’ll have a faster connection latency-wise, so if you need to game wirelessly on one of those platforms, it’s a better choice than the Arctis 3 Bluetooth.
Both feature a wired option as well, which you’ll need to use on the Arctis 3 for lag free gaming.
The headband difference might mean something to you but I think they’re both fine choices.