The two are very similar - though there is definitely a head game involved in the scariness of sports climbing. Bouldering can be very intensive in terms of sheer attempts on single moves and a single boulder. There are a huge amount of cases where a specialist who focuses on the other does amazingly. For instance Adam Ondra can boulder 8C+ / V16 and Ashima Shiraishi has climbed 9a/9a+. The "best climber" really is more about choice of time in these cases.