The big advantage of a DI fed from the amp's speaker output with a loadbox replacing the speaker is that nothing is being attenuated - you're not reducing the output from the amp at all.
A better alternative to an attenuator that lowers the speaker volume is a lower powered amp. But a cranked five watt amp isn't much less loud than a 50 watt amp into the same speaker. It's half the volume, but for domestic purposes will easily carry through walls and floors. Lots of guitar speakers push out around 100dB with a 1 watt input.
The sub-one watt amps like the Blackheart, which uses a pair of 12AX7s, one in the preamp and one as the power amp for a total output of around 1/4 watt are more usable, especially with an inefficient speaker. Blackstar do a similar low-powered amp, though its drive channel seems horribly noisy. I've not tried a Z-Bex mini-amp because the high price and difficulty in obtaining replacement valves puts me off them.