M852 might be onto something with the sleep mode of the HM-10. It's low-power sleep mode appears to be somewhat different from the HC-06. Best way is to try turning it off:
HM-10 sleep auto sleep mode disable: AT+PWRM1
Either way I would suspect some difference between the two bluetooth modules. You can find datasheet for each of the modules here:
HM-10 : http://wiki.sunfounder.cc/images/f/f8/Bluetooth_4.0_BLE_module_datasheet.pdf
HC-06: https://cdn.instructables.com/ORIG/FQ1/CUVZ/HXA9PUVQ/FQ1CUVZHXA9PUVQ.pdf
Something else I noticed is that the HM-10 seems to be a Bluetooth Low Energy device which I don't find any mention of in the HC-06 docs.