Yes Smallaxe, the gas losses besides carbon dioxide and methane (which have little to do with soil plant nutrition) include hydrogen sulfide and ammonia. No other nutrients are lost through gassing (leaching is another story, but that holds true for both types of compost).
However, if using a pile with proper proportion of feedstock (C to N ratio) you don't have to worry about gassing off to much regardless if it is aerobic or anaerobic. And even if you do get the losses, they are relatively minimal.
No other nutrients are lost! The claim that "[anaerobic compost] is basically fluff it has been all used up and mostly gassed off" is exaggerated. Only two plant nutrients are potentially lost as gas and this loss is minimal.
Besides, you aren't applying compost for it's nutrient value anyway! You are applying it for its "fluffy", "nutrient sticky", and relatively stable organic compounds.
Now, growing a plant in media that is anaerobic is a completely different story. Don't confuse the guy by combining the two issues please (anaerobic digestion in compost, and anaerobic soil conditions). If you are going to apply anaerobic compost it is best to let it dry then turn it. This will allow the phytotoxic gasses to escape. Once incorporated into your soil you do not really need to worry about it returning to anaerobic conditions.
So again... YES use that compost! Just air it out before you do and you will be fine!