In the finance world, an important messaging standard is ISO 15022, otherwise known as "MT" or "MTnnn" messages. ISO 15022 messages are written using ASN.1, which is a document/message syntax that pre-dates XML, and is probably most widely used in the telecommunications industry. ASN.1 has never really caught on as XML has. I think a lack of low cost software for processing it, especially in its early days, is probably the key reason. ISO 15022 messages, and other similar ASN.1 messages that are supported by the SWIFT network, are widely used between banks and other financial institutions. However, I'm not aware of any financial institutions that uses ASN.1 messages internally. It is a bad future indicator for a technology if users support it at their boundary, but don't leverage it internally.
ISO 15022 is due to be superceded eventually by ISO 20022, which is XML-based. One of the big topics at the Sibos Standards Forum was how migration will happen from ISO 15022 to ISO 20022. In a nutshell, the companies that have already invested a lot of money in ISO 15022 infrastructure don't want to spend a lot of money to migrate to ISO 20022 unless they get something extra out of doing so, something to give them a business driver for the cost of the change.
It looks like that driver will be payments. Conceptually, "payments" is as simple as it sounds - one company pays another some money, usually in return for goods, services, stocks, bonds, etc. However, the complexity around payments is that there are many things that can go wrong, especially as payments can have strict rules for when/where/how the payment is made, and there are usually financial penalties for breaking those rules. If somebody owes you millions or hundreds of millions of dollars/euros/pounds/etc., you want that money to turn up on the day it is due, not a week later.
Payments aren't (suffuciently) covered by ISO 15022, so they are a new area where there is the business case for building the infrastructure for ISO 20022 and XML. Once the big players have that infrastructure in place, I personally expect to see an acceleration in the move from ASN.1 to XML, as those big players come to realise that there will be savings in moving to ISO 20022 and rationalising their infrastructure. Give it 10 years, though.