No reason to do one or the other, do both!
I have passive splitters on the antenna to feed 3 receivers at the same time, the homebrew tube superhet, the Icom 7610 and an airspy hf plus discovery.
The airspy runs on a big monitor and gives a lot of detail and allows sideband selection, sync detection, drag and drop filter, etc.
Pick any old boat anchor receiver and bridge the sdr along with it.
Listen to the nice tube audio (on the older radios) and look at the sdr...