Take care that you read and understand the data sheets correctly. For example, the ULN chips are rated for 500mA per channel, but not for all channels at 500mA at the same time. But for the TPIC chips, they might be rated for only 150mA per channel, but that's 150mA per channel for all channels at the same time. So how many channels you need to be active at the same time might guide your choice.
Another factor which may be important is voltage drop. The old ULN chips will probably drop 1.5~2V of the input voltage. At 24V this might not be much of an issue, but at 5V it certainly can be an issue. This voltage drop is because they use Darlingtons.
The newer TPIC chips use MOSFETs instead of Darlingtons, so their voltage drop is only a few tens of millivolts, making them much more useful at lower voltages like 5V.