Every time I use the upstairs sink the water drains out slowly, until an air bubble escapes (burps), then it drains more quick. The toilet also does not always flush completely (inconsistent). There is no burp. I have run a snake in both drains. The house has 2 floors and a basement.

Every time I use the upstairs sink the water drains out slowly, until an air bubble escapes (burps),
This indicates a blocked vent. If the lavatory vent were blocked it would affect the entire bathroom group. The solution would be to snake the lavatory vent from the roof. Put out enough cable to reach the base and 15feet more. Good luck, Tom