To put it another way, they're kind of the same thing as the RAND Corporation. Maybe more technical and less strategic?
MITRE operates FFRDCs, as mentioned elsewhere in this thread, with very specific roles and limitations. They also don’t do a ton of policy analysis - they mostly do technical and architectural work, and support program offices and system developers. So your comment about strategic vs technical is mostly accurate, but it’s a little more nuanced.
(I am a former MITRE employee who still thinks they do good work and fill an appropriate role)
Edit: I guess RAND also operates FFRDCs too, but on policy analysis.