Bitcoin Cash pros: A big argument for Bitcoin Cash is that because it allows for much larger blocks than Bitcoin Core, this will allow greater throughput (~24tx/sec max) & less backlog as well as lower fees. This lets Bitcoin Cash scale more and their argument would be it is more useful for peer to peer, for commerce and just everything. Additionally it does not include Segregated Witness (SegWit) (which some view as a positive since some see SegWit as less secure or having legal issues).

Bitcoin Cash cons: Against Bitcoin Cash we have arguments like it is more centralized due to small less well known development team and due to fewer people running Bitcoin Cash full nodes and higher cost to run a full node. It does not (yet) solve transaction malleability (SegWit) and so existing Lightning Network (LN) implementations won't be run on top of Bitcoin Cash at this time.

Bitcoin Core pros: Established large development team, robust network of nodes (less centralized), transaction malleability fix (SegWit) allows current Lighting Network to run on top of it. SegWit allows for double the existing transaction throughput of the current Bitcoin Core limit of ~3tx/sec to ~6tx/sec max once enough people are using SegWit style transactions.

Bitcoin Core cons: Even with SegWit transaction throughput is limited. Centralized control of development from Blockstream and very small group of prominent devs that effectively have control over changes. Some toxic developers. SegWit some believe is less secure or can lead to problems (this is of course highly disputed). Reliance on unproven solutions like LN to increase throughput/scale beyond block size limits.
(Note also that the Bitcoin Core chain may undergo a further hard fork later this year when SegWit2x forks off that chain. But no time here to describe those implications.)