I played viola for 6-7 years and always had this problem to a degree where plucking or playing a string made me feel the pitch was wobbling in a range. I assumed I just don't have a precise ear, but was just fine tuning using 5ths, i.e. playing two strings and listening for them to match against each other.
For guitar, sometimes I tune string by string, but then the relative pitches don't sound right sometimes. Sometimes I tune relative by playing the 5th (or 4th) fret of the lower string to match, but then I wonder if the precision drifts as I go from low E to high E. Sometimes I outright use a tuner with the gauge, but as much as the device reads correctly, I swear sometimes they just don't feel precise. (It's been a while since I tried the tuner so maybe I imagined it.)
For an unpracticed, or maybe just off-pitch, ear like mine, is it better to tune string by string against each pitch (play E, tune E, then play A, tune A, then play D etc), or better to tune one string then match relatively by playing the 4th or 5th fret of the lower string, or use a tuner? I've been tuning relatively simply because I prefer the strings sound good against each other than trying to tune each to a perfect pitch.