The mathematics are quite simple.
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For a non-condensing dryer (i.e. one with a flue pipe)
The hotter the exhaust gas, the more you're heating the exterior vs. heating the clothes. -
For a condensing dryer
The hotter the exhaust gas, the more you have to cool the flue gases before you can extract the latent heat.
Either dryer uses ambient air to its advantage - the condensing type may recirculate air internally but it is also running external air over the condenser HX continuously - otherwise it wouldn't condense. The non-condensing dryer derives a benefit from more ambient dry air being pumped through the machine and hence absorbing some of the moisture at the very low cost of drum rotation and blower use. In either application, the heat is the primary 'cost' of operation. So to the extent that you can maximize the heat being absorbed by the clothes vs. blowing it out to atmosphere (or into the house) you will benefit.