A comparison can be expressed either with genitive case, or with the conjunction чем meaning "than" with no difference in meaning :
Сестра красивее брата. Сестра красивее, чем брат.
In spoken Russian I prefer a short form when possible, but both are widely used.I said "when possible" because if I use менее +adjective, I say чем.
With the compound form (более,менее + adjective), the variant with чем should be used, you can't use genitive in this case:
Они – двойняшки, но сестра более активная, чем брат.
The construction with чем should be used with parts of speech which are not declined or with prepositions:
Сегодня день теплее, чем вчера.
Мороженое с клубникой вкуснее, чем с вишней.