Feint+EA vs. HS+EA

On Feint, part 1:
For the straight Feint+EA vs. HS+EA scenario, the latter is (very) slightly better.
Over a long haul of 168 GCDs, if you Feint every EA, in theoryland[1] you will have done 28 Feints, 28 EAs, 24 Jaws, 21 Straight Shots, and 95 Heavy Shots. On average, 18 of those Straighter Shots will be proc'd[2] and thus worth ~200 adjusted[3] potency. Given a 2.4s GCD[4], this is 30470p over 403.2[5] seconds, for 75.57 pps.
If you HS every EA, you'll do the same 28 EAs (still every sixth GCD, just a tad delayed each time), 25 Jaws[6] , 24 proc'd Straight Shots, and 119 Heavy Shots. 31590p over 416.64s (28 clips of .44s), for 75.82 pps. 0.25 pps better than Feint.
This is what I mean when I allude to Simpson's Paradox - while in isolation, a Feint-EA does more pps than HS-EA, in the context of broader GCD / EA usage, the latter has a better result. This is because HS-EAs lower pps is over a bigger "sample size" of 3s instead of 2.5s, allowing it more weight to raise the big-picture pps.
[1] ignoring a lot of other factors, as they should impact both scenarios being compared more or less equally, I'd think
[2] of course you'll probably use a couple more SS and a few less HS due to said procs, but if we ignore that in both cases it should be fair for the comparison's sake
[3] a proc'd SS can't benefit from crit chance, and we aren't factoring in crit elsewhere here so we reverse-account for it on the proc
[4] as noted elsewhere, changing the GCD doesn't greatly impact results as the HS-EA clip shrinks with a shorter GCD as well, unlike a normal double weave
[5] granted, over six and a half minutes of pure uptime is absurd, but this is theoryland, and Living Liquid did happen I guess
[6] it's not a guarantee, even in this long frame, that HS-EA will actually force you to do an extra Jaws, but I'm erring on the side of Feint-EA for completeness

[a] relevant but ignored, even if you aim to Feint every EA, sometimes you will have to IJ-EA or castSS-EA anyway. Other times an SS proc might align with an EA and save you a Feint. The latter also holds in a reverse sense for an HS-EA plan. These things counterbalance each other in a surprisingly even fashion, just tilted a tad in HS-EA's favor.
[b] the notion that some series of double weaves might allow a slightly earlier EA than the theoryland expects, is only a factor for HS-EA, as Feint-EA hits EA right on time normally. So it's a small boon for HS-EA that isn't accounted for.


Feint, part 2:
But what if you're talking about Feint into a double-weave'd EA? As in, Feint-BL-EA or Feint-EA-BL...
This flips the math, because now instead of HS causing a 0.44s clip, it causes a 1.23s clip while Feint causes a 0.54s one. A 0.69s gap instead of a 0.44s one makes quite a difference. In a magical land where we double weave every single EA, (making all the same assumptions including handwaving the specific choice of oGCD as moot) Feinting becomes 0.66 pps better in the scenario above, rather than 0.25 pps worse.
So ultimately it may come down to one's individual propensity for doing EA+BL plays. The question of whether it's best to do that double weave, versus sitting on BL versus sitting on EA, is almost dead even math-wise (unless you're oGCD backlogged), so it's kind of individual preference.
(Some folk even go for the dunk by Feinting after an EA where BL procs during its cast, hoping to hit the BL in Feint's sooner oGCD window before the next DoT tick comes, with luck getting to double BL. You need to have a very keen timing eye for that though.)
I'd tend to believe that doing the double weave is probably the best habit to develop, since sometimes you will be backlogged and it's certainly good there. If someone is of that mind, and especially if they also like to double weave things like SW+EA or RS+EA (and they ought to do ME+EA ofc), it's hard to argue that doing Feint-EA as a default is really going to hurt. River procs on about a third of DoT ticks these days, nevermind if IR is on your DoTs or you're multi-DoT'ing.
However, I'd nonetheless caution to try avoiding it while under buffs (i.e. Bar+EA under HEB4B), unless it allows one to meet some timing concern. The loss of choosing Feint is a drop in potency right-now, while the gain is a nebulous down the road maybe-get an extra Heavy Shot. If you're under buffs, that right-now loss is going to hurt more and still be very certain, while the future prospect remains the same.