This is a great question.
The TLDR is; Yes, Call Centers are generally less secure than online payments. The reason for this is because of the inherent human factor in a call center - e.g. saving payment card details into notepad to process later because the payment service is down (seriously!!!).
But, there are a couple of things to address here, 1. Payment security and 2. Call security.
To start with 2. Calls are encrypted both on their way to the bank from your Telco's PBX, and again once they hit the banks DMZ, with a thing called an SBC (Session Border Controller). This has been standard since the proliferation of VoIP tech in the enterprise environment. That said, the quality of said encryption isn't great (Base64??) and relies on an assumption that both your telco and the banks telephony team are applying patches to their kit, and upgrading it when needed.
On 1, the payments / banking industry has been at the forefront of understanding the importance of getting this sh*t right for a long time because it is such a huge risk for them.
The standard for secure payments processes / infrastructure / architecture is called PCI DSS. PCI DSS was developed specifically to provide consumers like us better security when making payments. All call centers including banks, must adhere to its standards. This also applies for any other payment "endpoint" such as in store or online payments.
There are different levels of PCI compliance based on how many payments you are processing each year. Even the lowest requires 4 random audits to be conducted each year for an organisation to retain their compliance certificate.
In fact PCI DSS is almost an industry of its own these days, with companies building infrastructure and payment services to take organisations payment services "out of scope" of PCI DSS by owning all the risk.
To answer your question specifically, some of the key things outlined by PCI DSS are:
- Never storing card data in plain text at rest - Tokenisation is used to overcome this.
- Never storing card verification ID's like CVV or Pin - Never ever
- Using the principle of least privilege
- For access to network services
- For access to payment GUI's (call center agents)
- For access to call recordings for QA purposes
- Ensuring transmission of cardholder data across public networks is encrypted - With standards like SSL / TLS
- DTMF Masking - so that if you do punch in your card number from your keypad, all the beeps are monotone
I don't have enough rep to post more than 2 links, but for a better overview of what's required for telephone based payments, check out this blog post.
So, banks and call centers may store some of your payment card information at rest, as long as it is tokenised, and stored in a walled off PCI compliant network. Further, you will have basic encryption provided at the call being made, and again inside the banks telephony network, plus DTMF masking during any keypad payments.
In summary, with these standards and practices, you are more secure from a technology perspective when paying with an automated service than when you are talking to a human!
Sorry for the long post! :)