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High drain.
Rechargeables are better at long slow drain unless you've got something like a 18650 which does the high drain rechargeable thing great (hence finding them in cameras, etc).
If it takes something like a AA then you'll typically get better performance from a non rechargeable lithium battery.
You didn't mention what format it uses. And idk why the battery dimensions produce different characteristics, it's chemistry obviously but my knowledge is limited to just ended consumer things picked up over years. If you want a high drain battery, short and fat beats long and thin for rechargeable, unless non rechargeable lithium based.
Velocio-
18650
Those are lithium-ion batteries (like in your phone, laptop or drone), and you'll never find an AA or AAA with a lithium-ion chemistry because the devices that use AA & AAA don't contain the under volt protection that li-ion batteries require. (If you run a li-ion battery flat, you've essentially destroyed it).
Typical AA & AAA chemistries (e.g. NiMH rechargeable and alkaline non-rechargeable) can happily be run down to 0v.
It seems very odd that @Familyman's device specifically advises against using rechargeable batteries. The device couldn't be damaged by the lower voltage of rechargeable batteries because alkaline batteries would also have those lower voltages at some point.
I bought some off-brand batteries in bulk recently. They were a lot cheaper, and I assumed they'd be worse but at least comparable to the branded batteries. But it turns out they were a total scam, and they went flat within days (when I'd normally expect them to last a year). @Familyman maybe you just have a batch of bad batteries?
cyclotron3k
The instructions make quite a few statements that rechargeable batteries must not be used - conspiracy to keep Energizer profits up?