So I've been playing some games online with this deck on untap.in - for those of you who don't know it's a free platform to play magic games online.
In testing, this deck is actually surprisingly competitive even with the janky combo in there. As with every deck, it has really good match-ups and really rough match-ups.
Seemingly good match-ups: Storm, elves, goblins, burn, Griselbrand, Bloomless titan
Even match-ups: Infect, Merfolk, Dredge
Really bad match-ups: Any type of control, Eldrazi, Jund/Junk
As for the good match-ups, they seem to make a lot of sense. A lot of the time, my wins didn't actually come from using the combo (as expected), however when I did win from using the combo, it came at the most unexpected times.
For example, in a game against a mono-green stompy, I was down to four life, had three cards in hand, and my opponent had 20 life. It was turn 6. I was trying to stall as much as possible (thanks to Lingering Souls for coming in clutch), and I had Angel's Grace and Spoils of the Vault in hand. I just swung full, he didn't block and I did the combo and won. A very unexpected and surprising win because I was dead next turn.
As for winning normally, I won with normal Death's Shadow play. Hand control with Thoughtseize and effective lifeloss, swinging with Death's Shadow and controlling the board with creature removal.
Continuing on with why I consider the good match-ups good is because Angel's Grace was a fantastic tool for me to stall out the game against combos.
When I went against storm, I wait until they grapeshot and then Angel's Grace. A good chunk of their ramp cards will be exiled due to using Past in Flames, and as well, cantrips will run scarce too. Angel's Grace will stall the turn out, and make me not die. In one game, I actually used Angel's Grace twice - once by regular cast, another time with Snapcaster Mage and I won the game because my opponent forfeited because he had nothing left.
This deck stumps most other combo decks for that exact reason - once the combo goes off, it's hard to recuperate if you don't win. In elves, which is a more turn consistent combo (meaning it can go off multiple turns in a row), you really just have to play the hand control game. Using Stubborn Denial on Collected Company, Lead the Stampede, and Chord of Calling, and then destroy their board presence by wiping out mana dorks. If Elves doesn't have mana dorks, elves doesn't win.
Dredge is an okay match-up because the deck tends to have very good creature presence. So it is really hard to get swings in with Death's Shadow. As well, removing creatures is very difficult because they tend to be quite permanent. There's quite a lot of graveyard play and in order to get swings in you have to exile their creatures.
As for infect, it's really a race to win. Angel's Grace does nothing in this match-up, and you're very reliant on controlling their hand and creatures to get the job done. If you have no counter spells or creature destroys/exiles or any hand control, you're likely dead. If you get one of the three, you can generally be in an okay spot and make it a really grindy game with Lingering Souls.
Merfolk is an okay match-up because it has the same plan as you. Beatdown, but the difference is that merfolk is generally mono blue, so it's going to run some aspect of control. This can really shut you down. But sometimes if the opponent doesn't get it, you can get a very easy win.
Bad match-ups are pretty easily explained. Jund/Junk, control, and Eldrazi run some aspects of control. Thought-Knot Seer and Thoughtseize and Inquisition of Kozilek really make your life hard. As well as hard counterspells, and turn stallers like Remand make it even more difficult. Any type of control will generally win because you won't get out a Death's Shadow (they won't let you), and if it gets seen in a Thoughtseize or Inquisition of Kozilek, it's generally your opponents first choice to take away anyways. So life gets very difficult against control.