I'm not sure that anyone can "verify", but I can offer an opinion.
In theory, the 30-pin output jack should be better, although whether you personally will notice the difference between the two will be down to your preferences and your hearing.
But there are several other things to consider:
- does the battery on your Classic still have enough power to run usefully and for long enough. Plus, how much longer will it do so? If you browse the discussions here (for the Classic) I think you may spot several threads about this. Here's one: battery - Apple Community
- following on from the point above, the Bluetooth adaptors that I've used (the 30-pin dock connector ones) all get their power from the iPod, so if your iPod's battery is already weak due to age, will it be good enough to power the adaptor as well?
- how much longer will the hard drive in the iPod remain functional? Again, there are posts in the community about Classics that have failed hard drives. Here's one on that issue: my iPod classic shows an x with circle ar… - Apple Community
- can you find, at an acceptable cost to yourself, a Bluetooth adaptor that has a 30-pin dock connector that plugs into the iPod Classic? They are still available, here in the UK at least, but what about your country and at what cost?
The two discussions I've linked to are both from the 15th December, just a few days ago.
The drive on my iPod Classic failed. I've had to move on.
