It's situational. I think in general, it's better to use sql to get the exact result set.
The problem with loading all the entities and then searching programmatically is that you ahve to load all the entitites, which could take a lot of memory. Additionally, you have to then search all the entities. Why do that when you can leverage your RDBMS and get the exact results you want. In other words, why load a large dataset that could use too much memory, then process it, when you can let your RDBMS do the work for you?
On the other hand, if you know the size of your dataset is not too, you can load it into memory and then query it -- this has the advantage that you don't need to go to the RDBMS, which might or might not require going over your network, depending on your system architecture.
However, even then, you can use various caching utilities so that the common query results are cached, which removes the advantage of caching the data yourself.