Consider the difference between external and portable drives.

External drives use a separate power supply.

Portable drives are powered from the computer's USB port.

The cost/GB is about double for the portable drives, and they are almost always slower (5400 rpm vs. 7200). Advantage of portable drives is that they are, well, portable. External drives will be larger, and more fussing required because of the power brick, cord, etc.

Some (many?) older laptops don't have enough power in the USB port to power the portable drive. Some drives come with a two-headed USB connector, so you can use two USB ports if needed to adequately power the drive. Additionally, some drives have an optional power port too (Simpletech allows for both).

Recommendation? External, not portable, because I have had reliability problems with a significant percentage of portable drives I've purchased.

For the most part, I would not consider a portable drive as suitable for backup of critical files.