Both methods produce accurate results, though they measure different aspects of sea-level rise. Both show, for example, that sea-level rise is accelerating. But tide gauges provide direct observations, over 75 years or more, for specific, sparse points on Earth’s surface.
Satellites cannot yet match this long-term record; the altimetry record so far is just shy of 30 years. But satellites provide something tide gauges can’t: nearly global coverage, more thoroughly recording planet-wide trends and explaining the changes behind them.
Satellite altimeters can measure the height of the ocean from space to centimeter or millimeter accuracy when averaged over the globe. Both measurement methods capture regional trends in sea-level rise, and tide gauges also can provide an approximation of global trends, helping to calibrate satellite measurements.