The best advantage for supreme court judges is that they are uniquely positioned to defend the constitutions and help overcome the tyranny of the majority. Because they are not elected, just appointed by the Senate, they cannot make decisions based on the wishes of the public; as the right decision is sometimes neither easy nor popular. Federal judges also don’t have to worry about raising campaign money to fund their re-election and to keep their jobs, due to their appointments.
Some disadvantages for supreme court judges being appointed rather than elected is that judges are selected ‘behind closed doors with no accountability’, or so it can feel like to the public. The news following our most recent appointment of judges happened very publicly, although with not much accountability. Life appointments mean that a judge, once elected, decide when their job ends, not anybody else. If a judge is appointed to the Supreme Court, the only way to get rid of them is to impeach them because of those lifetime appointments. Lastly, a disadvantage of having lifetime appointments for Supreme Court judges is that the world changes, and the judges do not change with it.