when you bought them, were they called "flexible hoses" or were they called "tap connectors?"
A tap connector has a nut on one end that screws onto the bottom of a tap.
Both of them usually have a connector at the other end intended to fasten to a copper pipe.
I can't quite make out the connector on your new flexy to see what type it is.
You don't have a copper pipe, you have a ball valve which is also intended to connect to a copper pipe.
If you are fond of plumbing, you could insert a short pipece of copper pipe between the ball valve and your hose end
Or you could take off the ball valve and fit the flexy onto the pipe
Or you could get a different tap connector which includes a ball valve, take off your old ball valve and fit that onto the copper pipe.
Your old ball valve looks like a budget version, which may leak now that it is old and has been used, so I think the last option would be best. Have you got a set of wrenches, and do you know how to turn off the hot and cold water supplies to your taps?