Well, I can provide some impressions of the portable amps I've tried with the Atrio...
1) Qables iQube - neutral, naturally expansive soundstage, detailed without harshness, deep and powerful but controlled lows. Best portable amp I've heard. I wish I could afford one.
2) Headamp Pico - similar to the iQube, with slightly less expansive soundstage and weaker lows (not weak, just slightly weaker than the stellar iQube), but still remarkably neutral and a good pairing with the bass-heavy Atrio, especially given that it's about half the size of the iQube *AND* can contain a built-in 24-bit USB DAC. Great buy for increased portability
3) iBasso D1 with v2 opamps - haven't yet gotten to compare this with the Pico or iQube directly, but the sound signature is similar to both (from my memory at least). It's beastly (bigger than the iQube), but is the most flexible amp around (save for the far more expensive Headroom Micro Portable) given it's built-in Cirrus DAC chip and TOSLINK, USB, and line inputs. Paired with it's internal DAC, this can be a bit sterile with the Atrio, but when fed from the line-in by my Monica 2 DAC, it's just fluid and lush. The amp section alone is lovely, the rest is gravy. Just a shame it's so big and not terribly pretty. Good match with the Atrio, though, and I suspect the various D2 amps would be as well (just no TOSLINK, so useless to me).
4) Ray Samuels Tomahawk - My first portable amp, and a damn good one. While designed for IEMs, this was really more intended for use with brighter IEMs (especially the Shure E500, according to Ray's posts). The bass is deep to the point where it just borders on muddy with the Atrio. The soundstage is nice, but seems somewhat flat compared to the iBasso D1. Still a wonderful amp with very good sound and insane battery life, but not the best choice for Atrio users (the Pico would be better if aiming for a similar physical size). Still, you could do far worse...
5) Headroom Micro Amp - I tried both this and the Tomahawk with the wonderful Micro DAC back in 2006(?) and the Future Sonics EM3, the muddier grandparent of the Atrio. The Tomahawk was wonderfully revealing, clean, and powerful, while the Micro Amp sounded like a muddy mess. This might pair well with the harshly analytical headphones that Headroom champions (Etymotics ER-4, AKG K701), but it sounds awful with Future Sonics earphones. So due to poor synergy I do NOT recommend it, or the new Micro Portable, for use with the Atrio.
6) Mini3 - Hey, for about $100 it's a decent amp. Not nearly as good as the Tomahawk in any respect. Definitely a case of You Get What You Pay For here. Better than no amp at all, but you can do much better.
Now, I did try out a couple other amps, including the Lisa 3, but wasn't able to do as careful and controlled comparisons in order to get meaningful impressions. But in the end, my biggest recommendations for amps for Atrio owners would be the iQube or the Pico. Or both for different purposes, if you can afford it. The iQube is the best portable amp I've heard to date, and pairs perfectly with the Atrio. The Pico, while not QUITE matching the iQube as an amp, is still an absolutely stunning amp, and a far more versatile one given it's incredible size and potential for built-in DAC. I recommend both equally for use with the Atrio.