Choosing the right fret for you, thick or thin, short or tall, depends on the sound and feel you may like. Earlier guitars (acoustic and electric) came with little variety in fret size and style. Today, guitars come with many different frets or wire style ad shape. It would be important to know the difference. Fret wire is now available in three (3) shapes, round, triangular, and squared. The most common fret profile would be round head or "bead". Lower, or flatter frets, produce less drag when moving up and down the neck. They are easier to note. Round or oval type wire would have different heights, widths, and advantages over other shapes of wire.
Tall wire would range from .050" to .065" on the crown height above the fret board. The advantages of taller frets are that they are easier to bend because your fingers are in less contact with the fret board. Plus you have more sustain because the strings are in more contact with the fret wire than the wood fret board which would dampen the sustain. Taller frets outlast lower ones.
My viewpoint would be that taller, larger frets have so many advantages over shorter frets, and once you have used taller frets, intonation and tone will improve. Relax your touch and the frets will feel better.
Sometimes, for a number of reasons, intonation can be greatly increased by moving or reshaping the top of the fret crown. Moving the crown's peak forward will raise the pitch, and moving the crown back will flatten the intonation. Doing this can make intonation nearly perfect.
Frets may come in 12% nickel or harder 18% copper, nickel, and zinc. Fret wire is not made of silver.
Frets began as round semi-hard wire that is heated to anneal, or soften, it. Then it is cooled and drawn through a roller die that compresses the wire into a fret shape.
Frets can be reshaped over time to repair wear, but with enough playing will someday have to be replaced. Play on.