You are probably hearing the front differential (if the other front wheel turns in opposite direction). The spider gears can be noisy (especially if straight cut gears). Normally, engine noise hides gear noises.
What is the fluid level. There should be a site glass on the axle tube. When I changed mine, spinning the axles produces some noise, but I would not call it loud. Just a clicking sound.
Hope this helps.
The fluid level was showing normal in the site glass. When I've changed the fluid in the axle I've used hydro fluid since that was what was in there originally. Gear oil would probably make the gears sound quieter.