Have owned an etrac and CTX with several thousand hours on them and got an Equinox 800 last week. People have mentioned some of these but here are my thoughts:
The ETrac/CTX will give you more target info with the CO and FE numbers so cherry picking is much easier. I feel it also has a much more stable and accurate target ID, especially when targets are very deep. If you have loose soil where coins go very deep there and you want to be able to cherry pick in low-medium trash sites I'd say go with E-Trac/CTX but only if this is your #1 Goal.
EQ 800 recovery speed is SOOO much faster than etrac/ctx so in trashy places it blows etrac/ctx away. That is just my experience with the stock coil I can't even imagine the possibilities with a sniper coil at high recovery speed.
EQ 800 is far superior for beach hunting than the etrac/ctx if you're looking for gold targets. It will get better depth and also find smaller targets like gold chains, earrings, and toe rings that the etrac/ctx will miss. I did some initial air testing and got a repeatable signal at TWENTY ONE INCHES on a medium sized gold nugget ring
I'm not kidding here. I tested the etrac at 27 sensitivity in all metal mode and got... wait for it... 15 inches.
Did I mention EQ 800 has gold mode for prospecting? Doesn't exist on etrac/ctx. While air testing I got the maximum depths for coins and gold in gold mode because of the true threshold, and high sensitivity. I haven't meddled with it yet but gold mode may be able to get some extreme depths on coins and I'm suspecting that advanced users will eventually figure out how to make that happen.
The EQ 800 is way lighter than the other two machines.
The EQ 800 Costs less than the other two machines.
To answer your question:
I'm guessing the conditions where the ctx would be favorable, are locations where better target identification is necessary.
--- Yes, but we're talking about cherry picking silver dimes from clad dimes here. For general detecting you will be able to dig the coins signals most of the time on the eq 800. For beach detecting you will be digging a very wide variety of targets and the target ID doesn't matter much, especially if you're seeking gold only.
What real world locations would have those conditions for success?
--- Loose soil, deep coins or when you have enough hours on the machine to be able to determine clad from silver if you want to do that.
Would that be a park location with old silver covered by decades of soil and modern non-ferrous trash?
--- No. Both CTX and etrac have slow recovery speed so high trash areas are not their strong point. EQ 800 will run circles around them in high trash areas.
Could you disc/notch out that top layer of trash at 1-3" and just hear the deeper target tones?
--- Not really. It's pretty much impossible to get deep targets at a place that has a top layer littered with trash. Your best bet is to have a high recovery speed and get in between the bad signals to sniff out the good ones and find good targets close to bad ones.
Also, assuming the ctx has a bit more depth, especially with the larger coil, at the beach where targets might be sanded in a bit, you would prefer a ctx?
--- Nope. Assuming you're going to the beach for gold then EQ 800 will be far superior, even at depth.
Not trying to be an advocate of the EQ 800 already but from what you're describing the EQ 800 might actually be better for what you're trying to do so lightweight and cheaper are just a bonus. If you came to me and said Cutaplug I want to find super deep coins in low trash areas and not dig very much trash then I'd say CTX. GL with your decision =)