Constantin:
For me, it came down to convenience. The TXB series is great if you have lots of of signal lines at one voltage being shifted to a different one - add a single TXB and you're done. Very clean board layouts can result and space savings are possible for any layout with more than 4 lines.The BSS138 approach works great for single lines or when you don't mind the complexity that having three chips (BSS138 and two resistors) adds for each signal line. It's also great if you have lots of voltages to contend with - 1.8V, 3.3V, 4.2V, etc.
Where the TXB chips won't work is for I2C signal lines. They need a different translator, the TXS01xx series.
The other problem with the TXB series is the driving IC has to source at least 2mA on the drive signal for it work properly. I ran into this issue trying to convert the signal from a GSM chip which couldn't source that high of a current. The TXS series has the advantage of working both on I2C (open-drain) signals and push-pull configurations (as long as the speed is below 20MHz).