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Even though both of them are frequency standard, and both are used simultaneously in almost every apex meteorology institute to keep the time, the cesium atomic clocks are more used in this field what is the advantage of cesium atomic clock over the hydrogen maser?

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The cesium clock has a better long term stability, while the hydrogen maser has a better short term stability.

From The hydrogen maser and cesium clocks in time keeping at NTSC:

Abstract:
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It is well known that the advantage of a Hydrogen maser is concentrated on its short term stability; however its frequency could drift when it runs for long term. The advantage of a cesium clock is its long term stability; however its short term stability is worse than that of a hydrogen maser. In addition, clocks, even though are of the same kind, their performance could be very different because of their noise and other factors.
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    $\begingroup$ But why is the stability different? $\endgroup$ – Sharun Shaji Jul 1 '19 at 10:48

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