Will running a pruned node make my store less secure?

No, not at all.

I was wondering what will be the downsides to me running a pruned node?

With a pruned node you cannot:

• Handle (extremely) deep reorganizations (which are in theory possible but in practice would indicate a very serious problem with Bitcoin's security assumptions).
• Serve old blocks to other nodes.
• Rescan for old transactions that may affect your wallet after importing an old address/key.

I'm not too sure why I need a full copy of the blockchain.

You generally don't, apart from the cases listed above.