In passive connection mode, DC++ will only make outbound connections to other users. All searches will be sent through the hub, and search results will be returned through the hub as well. DC++ will return a maximum of 5 search hits for a passive user. Passive users may not able to download from other passive users. Passive mode is an extra strain on hubs, so please do not use it unless you must. To find out what DC++ users are in passive mode in a hub check their tag in the list of users. Passive users will have M:P in their DC++ tag.
That being said, active mode on DC++ will make inbound and outbound connections to other users. While all searches will be sent through the hub, search results will be returned directly from active mode users and through the hub for the passive users. Active users can download from either active and passive users and get more search results. Obviously that means you can connect to a larger group of people.
However, there is ZERO difference in download/upload speed between active or passive modes.