It depends on how you handle both.
Under equal situations both will have the same amount of dust, BUT with 35mm you will enlarge that dust more than with MF, so it will be more visible.
Dust is an ever present problem especially with smaller formats. The enlarger needs to be clean. I use a small vacuum cleaner and canned air to keep it clean.
When not in use it should be covered with a plastic bag or other suitable covering. The negatives need to be cleaned as well. A small anti-static brush works well for most negs. For negs with finger prints or other grime film cleaner can be used sparingly to remove the offending particles.
Yes, everything in the darkroom must be kept clean. I use an anti-static cloth to wipe the negatives just before putting them in the enlarger. The darkroom also needs to be an animal free zone. I love my Corgi, but he's banned from the darkroom.