I understand that they both mean I do not like, but I'm not sure what exactly 「好きではない」means. Moreover, does the particle 'では'make a difference, or could you have just used 'は'?
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Actually they are equal --> じゃ（JA)＝では（DEWA）Not only you may find 「じゃ、では」ないです, but also「じゃ、では」ありません and their level of formality differs:
じゃない → most informal
ではない → more formal
じゃありません → more formal
ではありません → most formal
では is used in more formal situations. It really depends on the context, who you're speaking to, and how formal you want to be. For more information on their usage, you can visit [this page]