The 1928 Hawaiian (European) Discovery Sesquicentennial Half Dollar known to collectors is the result of two talented artists. Juliette May Fraser was the artist who prepared the coin's original design sketches and Chester Beach was the artist-sculptor who took Fraser's sketches and created the 3-D models that were used to produce the coinage dies.
For the obverse of the coin, Fraser featured a left-facing portrait of British Captain James Cook, the "discoverer" of the islands (from the European perspective). On the reverse, she presented a Hawaiian warrior chief (Kamehameha I, though unnamed). He is shown looking out over a part of the Hawaiian shoreline with an outstretched right hand indicating "Welcome!" In his left hand he is holding a spear. (I've always wondered how "sincere" the "Welcome!" actually was!

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Beach was faithful to Fraser's designs, but did make a number of minor changes (in addition to filling in the necessary 3-D details of the design elements):
Obverse
Fraser included the dual anniversary years - "1778-1928" - at the lower rim, centered on the six o'clock position. Beach moved the dates to the reverse and placed "HALF DOLLAR" in the same position.

Beach enlarged the motto "IN GOD WE TRUST" but kept it in the same position.

Beach added a compass rose after "CAPT."

Beach enlarged the inscription "DISCOVERER OF / HAWAII" but kept it in the same position.
Reverse
Beach enlarged and re-positioned "E PLURIBUS UNUM" - Fraser placed it just below the Chieftain's outstretched right arm.

Beach replaced Fraser's ": HAWAIIAN : HALF : DOLLAR :" with "1778-1928" at the lower rim, centered on the same six o'clock position.

Beach added the coconut tree seedling at the seven o'clock position.
Overall, I think Beach's changes were well done and made for a stronger and more balanced overall design. He was simultaneously true to Fraser's intended designs, while "punching them up" based on his experience as a sculptor and coin/medal designer. IMO, it was a good, effective and successful pairing!
1928 Hawaiian (European) Discovery Sesquicentennial Half Dollar

For more on the coin's "Hawaiian Chieftain," see:
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Quick Bits #15 - The 1928 Hawaiian ChieftainFor other of my posts about commemorative coins and medals, including more on the Hawaiian half dollar, see:
Commems Collection.