Migration from Sybase to a different platform
How feasible it is move the Sybase database to a different more popular platform such SQL Server or any other.
Is it feasible in the first place?

Very feasible and supported by the vendors (e.g. Microsoft in-case of SQL Server). I have done plenty of SybaseASE to SQL Server migrations.
Best is to use SQL Server Migration Assistant (SSMA) for migration.
Refer to :

Migrating from Sybase ASE to SQL Server – How to use SSMA for Sybase
SQL Server Migration Assistant (SSMA) Team's Blog


Which one is preferred?

Its up to your business what RDBMS they want to use. We are a Microsoft shop running majority of our software on Microsoft stack and so we move our Sybase Clients to SQL Server.
If you have any specific step that you find hard to proceed further, let me know and I will help you out, but above links will give you  a good start.