Some of the difference seems to hinge on how much weight to put on the immediate impact of QE announcements (when long-term rates tended to fall) and subsequent movements during the QE program (when rates tended to rise, sometimes after Fed announcements). This graph is from their paper:
On theoretical grounds I tend to side more with Gagnon's results; I don't see why QE would affect long-term rates with a lag. But I'm not highly confident in that view, and I think there is a decent possibility that Greenlaw, et al, are correct.
My bigger problem here is with the way the empirical findings in all of these studies are being interpreted, which to me seems like "reasoning from a price change". I can't emphasize enough that you cannot draw any implications about the effectiveness of monetary policy by looking at interest rates. Lower interest rates might reflect monetary stimulus (liquidity effect) or they might reflect monetary contraction (income and Fisher effects.)
As a practical matter, the main way that the Fed influences interest rates is by influencing NGDP growth (as well as NGDP growth expectations). Thus in 2007-09, Fed policy became increasingly contractionary, and this depressed NGDP growth. The slower NGDP growth led to lower long-term nominal interest rates. This was tight money, despite the falling interest rates. (And no, I'm not making a NeoFisherian argument.)
Even if Greenlaw, et al, are correct about the effect of QE on long-term bond yields, it doesn't tell us anything about the effectiveness of QE in boosting aggregate demand. Indeed an extremely "effective" QE program (think Venezuela or Zimbabwe) would certainly cause long-term nominal interest rates to soar much higher.
Elsewhere I've argued that it makes no sense to ask, "Is QE effective?" It's like asking whether a shovel is effective. How is the QE being used? If it's used to implement NGDPLT, and the central bank employs a "whatever it takes" approach, then of course it's effective. If it's merely a temporary monetary injection, as in Japan during 2001-06, then of course it's ineffective. QE is not itself some sort of policy, it's just a tool. We should be asking whether the policy regime is effective, not the tool.
PS. I'd also like to address this point:
The Swiss National Bank tried to commit to a target exchange rate, but gave up in January 2015. When it did give up, the franc appreciated 30% against the euro in a day, leading to a capital loss to the Bank of 50 billion francs. Svensson (2003) argued a binding commitment to price level target path, a currency depreciation with a crawling peg, and an exit strategy could produce a "foolproof" way to avoid a deflationary spiral for an economy stuck at the zero lower bound. However, it's not clear how real-world policymakers can or should bind themselves to such commitments. Continuing to make ever larger purchases in an effort to achieve a target that might prove to be fundamentally infeasible sets the central bank up for an arbitrarily large capital loss when it eventually capitulates.
This gets things almost exactly backwards. The large Swiss balance sheet was not caused by the exchange rate peg; it was caused by Switzerland's strong franc policy. When the SNB made the mistake of revaluing in 2015, they made the Swiss franc even stronger. At the time, I predicted that the balance sheet would get even bigger as a result, and that's exactly what happened. If the peg had remained in effect, the SNB's balance sheet would now very likely be smaller than its current value (which I believe is nearly 100% of GDP) and the SNB would not have needlessly suffered a 50 billion Swiss franc capital loss. Back in 2015, some pundits who had a similar interpretation to Greenlaw, et al, suggested that the Danes also might be forced to revalue. Instead, Denmark made the sensible decision to not revalue the krone, and hence did not suffer large capital losses.
BTW, Switzerland's tight money policy of 2015 resulted in lower interest rates, just one more example of why you do not want to look at interest rates to test the effectiveness of monetary policy.