I'd say histopathology is probably the most 'diagnosis/problem-solving' oriented specialty. The workload is a few cases a day, where you get all the slides and mull over them. Then ordering immunohistochemistry/immunoflorescence/cytogenetic analysis/PCR as needed. As a trainee, you're also receiving the specimens and dissecting/choosing where in the specimen to make slides from.
Things like haematology offer a half-way house between pathology and internal medicine. You'd see and assess the patient in the ward/clinic, but also look at their blood film/order further lab tests. But I think nowadays, the more complicated bone marrows and definitely lymphoma biopsies are going to histopathologists specialising in haematopathology.
That said, I still think the problem solving in clinical heamtology is interesting in its own right! Some internal medicine specialties are also pretty heavy on it - neurology and renal I reckon to name a couple.