Whenever I use a 1/4" DC endmill - I get a horrendously loud whine from the spindle cutting. I’m using factory speed n feeds.
The 1" surfacing bit does the same.
I can feel the vibration in the whole machine- but what can I change to at least tone down the noise?
What spindle do you have. If other bits do not do that is it possible the two bits in question are rotating out of round. Could they be bent or could your collet be dirty. I use a 4" OAL 1/4" bit at times and I usually have to reseat it a few times to keep it rotating round. Because of the long length in my Dewalt router the bit vibrates and will eventually loosen the collet. So start by cleaning your collets. I use brake cleaner and a brass bore brush to clean my collets. You would also need to clean the inside of the router shaft. Dust and gunk can accumulate and cause your bits to rotate out of round.
On the 1/4" bit roll it on a flat surface to make sure it is still round. The bigger bit would be hard but you could try to roll just the bit shaft to see if you get any out of round condition.
Some bits just make more noise than others because of the geometry of the cutting edges. Not saying that is your problem but the vibration would indicate the bits are turning out of round. So start with basics of cleaning the router shaft and collets.