It's more about the wattage than just having a big battery mod; the two you mentioned come in 3.7v and 5v/6v versions. At 3.7 volts, a Bloog carto is about the same on those mods as it is on a BMF battery.
At 5 or 6 volts, my guess is that a Bloog carto would burn out pretty quick or, at least, taste like it had. I haven't tried it, and I'm not gonna - you go first!
My understanding is that the "sweet spot" for most juices is between 6 and 8 watts (a matter of taste, of course); a Bloog carto on a 5v device would be about 10 watts and on a 6v device about 14.5 watts. For comparison, it's a little over 5 watts on a BMF battery.
Ideally, Bloog would offer low resistance cartos in the 1.8-2.0 Ohm range (I believe this possibility has been discussed) and that might give you better TH and a warmer vapor. Of course, it'll also burn through juice and batteries faster and not everything tastes better with more heat.