ghosthouse,
I think the comparison between the F-1 and he Eitr is very appropriate because they both have identical functionality, and very similar prices.
I've been using the F-1 for about 6 months, and it's a very good unit. I liked the fact that is was bus-powered and didn't require a power cord like the Eitr does.
Sonically they are very close. I notice a slightly wider stage with the Eitr, and better clarity in the highs, specifically cymbals. This was most noticeable with my Stax headphones. I also think that the Eitr has deeper bass.
But with a different source/speakers, etc, your findings could be the opposite.
I think you could be happy with either one, given the compact size and the price-point, but I give a slight edge to the Eitr.