Would You Rather Own A Good SET Amp, Or A Great Push Pull Amp?

I don't know how anyone can answer this conclusively, or for you, every situation entirely unique, variables go on and on. To start with how do you define great vs good, why a great push pull vs only a good SET, why not great to great? If your criteria for great is price, this may not hold for SET. There are many boutique/small operation builders of SET amps, they can custom build you an extremely high quality amp for relatively low price. 

Personally, I've had a number of push pull and SET amps (2a3, 300B, 845) over the decades, thus far SET for me. These days only mono blocks with quality transformers and power supplies, both critical for SET. EL34 my fav push pull tube, very nice mids, still don't compare with immediacy, illusion of performers in room SET is capable of. On the other hand just received Bendix 6094 mono blocks (EL84 iteration), these 12wpc push pulls, reportedly EL84 most closely resemble SET with more impact, we shall see. Bottom line, so many variations of tube amps, only you can determine what's best for your situation.

@ghdprentice + 1 - For me, I care a lot more about how I enjoy the sound than how it got to sound that way. 

I have a great SE 46 amp and several great PP amps.  I prefer each of the PP over the SE.

I’ve had both, including a 75 watt Allnic amp that supports switching from SET to PP. I’ve a large sound treated listening space. With my Tannoy speakers and Studer open RTR, I prefer PP. Stronger bass, deeper soundstage, more dynamism, and greater low volume detail were observed with PP. 

I owned both PP & SET tube amps over the last almost 40 years w/ several different speakers in different rooms. There’s no hard & fast rules about any of them but the midrange detail & realism of a good SET amp is tough to beat at lower to maybe moderate volumes even w/ high sensitivity speakers. They do run out of gas quickly though when pushed at all & the distortion increases rapidly beyond their power rating or even sometimes that their rated power. They have no real “headroom “ . I have landed on PO amps for that reason as I enjoy loud volumes at times & have a big room.