Diameter was designed to supersede RADIUS. There is no doubt Diameter provides superior functionality. Unfortunately, upgrading old RADIUS environments can be tricky.
“There is a large RADIUS deployment base out there and unless a proper migration plan that includes deployment of translation agents and co-existence of RADIUS and Diameter, migration to Diameter will not be simple.” 
The “translation agents” mentioned above are software or devices acting as adapters between new Diameter servers and legacy hardware that only supports RADIUS. Translation agents could relieve the effort required to upgrade, but they bring their own problems too.
“... there can be many variants and implementations of translation agents in proprietary non-IETF manners. Also due to the simultaneous standardizations of RADIUS and Diameter, various RADIUS messages may be handled differently by different translation agents along the process, while none of those translation agents can be assumed to have access to complete and accurate session state information.” 
That sounds hard. So RADIUS extensions have proven to be the easier option.
“… The uptake of Diameter has been very slow though, and RADIUS still remains the de facto standard for the foreseeable future. A major reason for this is probably the fact that the many enhancements that Diameter was supposed to bring are already covered by the various RADIUS extensions. There is, for instance, the RadSec protocol that transports RADIUS over TCP and TLS.” 
Of course, there are limitations to RADIUS extensions. Diameter can provide far superior support for 4G LT-Advanced mobile networks, for which RADIUS would be a very poor choice .
TACACS+ is also available, but
“TACACS+ overall function is similar to that of RADIUS but RADIUS has enjoyed a more widespread use since it is not a proprietary (sic) of Cisco.“ 
Some also argue that TACACS+ is more suited to network administration than general network access for a large user base (e.g. ISP, Telco) .
I appreciate that some of my references are old and my be out of date. Although, I have recently seen new, small-scale network deployments choose RADIUS over Diameter/TACACS+. In these cases, the staff know RADIUS; extensions provide required security; and RADIUS has no ties to Cisco.
I think it's matter of time before Diameter overtakes RADIUS, but it's very hard to tell just how much time.
 Nakhjiri, M. & M., AAA and Network Security for Mobile Access: Radius, Diameter, EAP, PKI and IP Mobility, Section 7.4, John Wiley & Sons, 2005
 van der Walt, D., FreeRADIUS Beginner's Guide, Packt Publishing, 2011
 Håkan, V., Diameter: Next generations AAA protocol, Institutionen för systemteknik, 2001
 Woland, A., RADIUS vs TACACS+, retrieved from http://www.networkworld.com/article/2838882/radius-versus-tacacs.html