Are some welding methods more hazardous than others in terms of welding fume generation?

Short answer, Yes certainly!
Long answer, There are welding techniques that pose risks in terms of fume production compared to others for sure. For instance, manual metal arc ( MMA ) or stick welding tends to release a number of fumes particularly when working with materials, like stainless steel. In the case of MIG welding the extent of fume generation can vary based on the type of metal and wire employed. Conversely TIG welding typically results in fume levels as it relies less on filler material. The materials being joined together through welding and the specific welding technique used can greatly influence the number of fumes produced during the process; hence it is advisable to be aware of the materials involved and ensure taking precautions as required.