You will want a high-drain battery (IMR or hybrid) for both the regulated and the mechanical mod.
A year or two ago I would have told you to get a protected ICR (Li-ion) battery for the mechanical for the additional mAh (battery time), and get an IMR (Li-Mn) battery for the regulated VV/VW mod. But battery technology has advanced for the better over that time. With the advent of safer chemistry batteries there is no logical reason to ever use a protected ICR battery in any mod again.
Now we have "hybrid" safe-chemistry batteries which are a chemistry mix of both ICR (higher mAh) and IMR (high-drain), with high amp ratings. The "best of both worlds" sort of thing, now you can have your cake and eat it too.
List of high-drain hybrid batteries with the highest mAh and highest amp ratings (applicable for sub-ohm
vaping):
Sony us18650vtc4 2100 mAh, 30 amps
Sony us18650vtc5 2600 mAh, 30 amps
Efest 18650 2500 mAh, 35 amps
* The Panasonic NCR18650 A (3100mAh) and B (3400mAh) hybrid batteries are exceptions to the above. They are not a high drain battery. Their chemistry is heavily weighted to be more like an ICR battery (with low amp rating of 6.8 amps and high internal resistance). These are not optimum batteries for mod use, but better suited for low drain applications such as flashlights.