Collecting data from source sensor nodes to designated sinks is a common and challenging task in a wide spectrum of sensor network applications, ranging from animal monitoring to security surveillance. A number of approaches exploiting sink mobility have been proposed in recent years: some are proactive, in that sensor nodes push their readings to storage nodes from where they are collected by roaming mobile sinks, whereas others are reactive, in that mobile sinks pull readings from nearby sensor nodes as they traverse the sensor network. In this paper, we point out that deciding which data collection approach is more energy-efficient depends on application characteristics, including the mobility patterns of sinks and the desired freshness of collected data. We illustrate cases where combining proactive and reactive modes of data collection is particularly beneficial. This motivates the design of TwinRoute, a novel hybrid algorithm that can flexibly mix the two collection modes at appropriate levels depending on the application scenario. Our extensive experimental evaluation, using synthetic and real-world network topologies and sink traces, shows that TwinRoute outperforms the pure approaches, achieving desirable tradeoffs between energy expenditure and timely delivery of sensor data.