Bitcoin is secured through proof-of-work mining using SHA256 as the mining algorithm. Bitcoin Cash uses the same algorithm, so the specialized ASIC hardware used to mine one coin, could also be used to mine the other.
PoW coins are susceptible to ‘51% attacks’, which are possible when a bad actor controls a majority of the network’s hashpower.
So generally, when considering ‘how secure’ a blockchain is, we consider how possible, or likely, it is for a single entity (or a group of colluding entities) to gain control of a majority of the hash power available for a coin. The more hashpower a coin has pointed at it, the more secure we can consider it to be. This is because an attacker would need a larger amount of hashpower under their control in order to enact an attack.
From fork.lol, we can see that over the last 7 days, the BTC hashrate has been approx 47.3 exahashes/second, while the BCH hashrate has been approx 1.6 exahashes/second.
By this measure, Bitcoin Cash is most certainly not ‘more secure’.
4Statements like "the world's most robust blockchain" are meaningless marketing fluff and should be ignored. But you can certainly read about how the currency works and draw your own conclusions about its security. The main ideas are the same as for Bitcoin, about which much more has been written. You can browse questions on this site, for instance. – Nate Eldredge – 2019-03-23T15:31:44.007