OK, I've got a little time to share some thoughts now, after a relaxing visit with relative and an old friend.
I ordered an Adams E3 and it arrived a little over a week ago. Subtracting my vacation days, I've had about a week to play on the horn now, which included a rehearsal with my regular accompanist, Sara.
Breaking in:
The horn and I are breaking each other in. I'm doing as I always suggest, taking out the valves each day to wipe them down and re-oil. I also ran a cleaning sponge through the leadpipe to get any factory residue out (there was some). After about 4-5 days the valves started to feel mostly normal. They are still not quite as fast as my "old" horn, but are workable now and getting better each day. I've played with the AGR, but I don't think I'm familiar enough with the horn yet to really know where to place it. For now I'm just going with the 2-full-turns-out setting, but that may change. The horn is getting a little more "open" in response each day, and my past experience is that after a month or so it is going to be around 95% as responsive as a well-broken-in horn. I'm still working on the right way to approach a few notes on the E3, because some are different from the E1. In concert pitch, the upper G does not feel quite comfortable yet. The high C# is easier to play, but I don't feel like I have it centered well for tone, mostly. But the high B is better than the E1, as are the high D, Eb, E, and F.
Intonation:
I ran a tuning chart on it today and the results on now up on the Intonation page on the main site. There are differences compared to the E1, and I don't know if I would say it's better, but it surely is different and I think it is easier to manage (kinda soon to say, really). See the attached image.
Build Quality:
The fit/finish on this horn is better than my previous ones, especially regarding the brushed finish. That effect is incredibly hard to make even as they brush around all the twists and turns of the valve tubes, but it's really quite a good job! The pistons have a nicer finish all around, which I like. All the tuning slides have a nice fit. And they are now buffing further down inside the bell, which looks better, too. See attache image (although the light-bounce effect makes it hard to see in the photo).
Tone:
This is really why I ordered an E3 to try. It was a bit of work to be heard over the civic orchestra I recently soloed with, and now and then I want more headroom in other settings. The E3 is definitely capable of taking more input and producing a larger sound when you want. It also has an inherently deeper sound, with more gravitas. The latter quality is attractive even in soft, pretty songs. I am still able to get an edgy sound when I prefer, without being forced to play louder than I want. Overall the tone is as flexible as the E1, which is a requirement in my book. Oddly enough, it seems even easier to handle during very soft passages - that's a bit counter-intuitive, given the extra capacity it has. Its wide dynamic range makes it easier to get the degree of expression I want. I hope you know what I mean - it's when you want to have certain notes jump out a bit more, or have a few notes at different volume from the line in general; it's all easier on the E3, which I was not expecting. When Sara and I did a rehearsal last week (on my 3rd day of playing the horn) she noticed the deeper sound and liked it.
Hug Factor:
The horn feels larger when I hold it. However, I can't quantify that. It fits in the Bonna case about like the E3 (might be a tiny bit tighter, but I can't even say that for sure). My Bonna case had both pads on the 4th-valve side, so it is outfitted like my E1 case is. I tried to measure its girth, much as you would measure a waistline when buying clothes. I tried to measure the length of a cord that went all the way around the horn, just above the 4th valve's position, and both horns where the same. However, I CAN say that the leadpipe angle is opened up a bit more now, so the horn is less parallel to your body front. This makes a more relaxed position for the right wrist and elbow, and may help a bit with projection (because the bell is effectively pointing out more). This angle makes a difference in fit to the case, because there is now no margin from the end of the leadpipe to the case wall (there was almost no margin before anyway, and I have not heard of any leadpipe damage during flights). Oh, and the reach to the 4th valve is about the same as the E1, but I think a bit shorter. (Having no good metric to use, I just measure the distance from the edge of the 4th valve button to the under-edge of the 3rd valve tuning, and their closest points. That should be a decent way to do it, I think.)
========
When I have a chance I'll do a couple videos. I'll probably record another piece with Sara in July, and I'm going to try to do an A/B comparison in my church's sanctuary, where the tone has enough cubic feet to do its stuff.