The choice of strings and the size (Soprano / Concert / Tenor) are probably the most obvious.
Design factors in construction, play their part also. Such design choices as the placing of the internal braces and type of kerfing employed can mean the difference between a uke that sings and one that, well, just 'plonks'
Visually the most obvious differences in ukuleles is the woods used in construction.
Woods are chosen for their Tonal Characteristics as much as their looks, perhaps even more so.
Kala Brand Ukuleles has produced this handy guide to Woods and the tonal properties they exhibit.
Some final words of advice ... Use Your Ears! We are all different, and much like taste in Artwork or Food we all have our own ideas of what is 'Good'.
Some people perceive a Bright Crisp Ukulele as Shrillness or Thinness, others perceive a ukulele with a big bottom end bass tone as 'Dull".
"Horses for Courses" as they say