This feels a little redundant (both cache specs implement similar code) and a little fragile (changing human-readable text in pht() generally should not affect program behavior, but it will here).

How about this instead?

Add these to PhabricatorCacheSpec (or pick some better names if these feel too clunky):

• private $clearCacheCallback;
• setClearCacheCallback($callback)
• getClearCacheCallback()
• (Optionally, isClearable(), which just tests if a callback is set, but maybe testing for a null return from getClearCacheCallback() would be good enough.)

Then, when building the caches, use $this->setClearCacheCallback('apc_clear_cache');, etc., to specify how to clear the cache.

This should likely extend PhabricatorConfigController instead.

It can then inherit the shouldRequireAdmin() implementation automatically, and doesn't need an explicit implementation.

Minor nit, but maybe define $cancel_uri = $this->getApplicationURI('cache/'); here to slightly reduce repetition, as this URI is hard-coded in three places in the remainder of the controller.

Consider naming the button "Clear Cache" for clarity.

Incorrect / redundant with the call below inside the ini_get() clause?

If one of these caches is missing but the other is present (e.g., we have OpCache but not APCu) I think this will try to clear a null callback and produce an error like this:

PHP Warning: call_user_func() expects parameter 1 to be a valid callback, no array or string given in ... on line ...

Likely fix is testing if the callbacks are set before invoking them.