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We are the beatdown here and they are the control deck, even though both lists are built on one-mana creatures. Most of our bodies attack the turn they land and nine burn spells finish from range, while their deck gets stronger the longer the game runs: tokens pile up from every death, Carrion Feeder grows with each sacrifice, and Rite of Consumption gains back the life we spent a game taking. So we keep pressing, and they block with creatures that leave tokens behind, trade off our attackers one at a time, and only switch to attacking once their payoffs have outgrown our burn. Speed and card quality favor us: none of their creatures has haste, Carrion Feeder cannot block at all, and late in the game our burn still hits their face no matter how many tokens they have. Resilience favors them: Nested Shambler, Infestation Sage, Nezumi Linkbreaker, and Shambling Ghast all leave something behind when they die, so a stalled board keeps adding to their side while ours just shrinks.
The race is ours to win or lose. Our hasty one-drops plus Lightning Bolt, Galvanic Blast, and Fireblast need to finish before Carrion Feeder and Mortician Beetle grow out of burn range and a Rite of Consumption drains us while gaining them life. Lead with a hasty one-drop and keep attacking: Reckless Lackey's first strike or Goblin Tomb Raider's two toughness wins most fights with their unpumped 1/1s, so the damage goes in before their sacrifices start growing anything. Gingerbrute is the best home for Inventor's Axe because none of their creatures or tokens has haste, so its 
ability makes it unblockable against their whole board; hold the Axe until blockers are declared, then flash it onto whichever attacker got through.
Burn has one job on creatures and one job on faces, and the timing decides which. Spend an early Galvanic Blast or Lightning Bolt on a lone Carrion Feeder or Mortician Beetle while they have no other creature to sacrifice in response; once a sacrifice outlet and spare bodies are on their board, burn aimed at a creature usually meets a sacrifice in response, the spell does nothing, and they still bank the counter, the pump, or the cards. From that point every burn spell goes to their face. Count their biggest creature's power as both damage to us and life they gain, since Rite of Consumption sacrifices it as a cost and our burn cannot stop the drain once the spell is cast. Every Snuff Out they pay four life for, in the lists that run it, brings them that much closer to our burn range.
Carrion Feeder is their main clock against us. It cannot block our hasty attackers, but it turns every spare body into a permanent +1/+1 counter, including a blocker that is about to die in combat, and then it becomes the creature they attack with and feed to Rite of Consumption. Do not aim burn at it while they have other creatures on the board: they sacrifice them in response, the Feeder grows out of range on permanent counters, and the Rite that follows is bigger for it. Kill it while it is alone or leave it alone.
Rite of Consumption is their finisher and their lifegain in one card, since the sacrificed creature's power is both dealt to us and gained by them. A grown Carrion Feeder or a pumped Bloodthrone Vampire pushes their life back out of our burn range in the same spell that drains ours. Do not wait to burn the big creature until the Rite is cast: the sacrifice is paid as a cost, so the drain and the matching lifegain resolve regardless. Burn it earlier, but only when they have no spare creature to grow it in response.
Bloodthrone Vampire is their best blocker against us. Each creature it eats gives it +2/+2 until end of turn, so with one spare body it beats Reckless Lackey's first strike or a Goblin Tomb Raider in a block. Attacking either of those into it while they have a spare creature is the trap: they block, sacrifice the spare for the pump, and the Vampire survives while our attacker dies. It also serves as the free outlet that lets them sacrifice anything our burn targets in response.
Mortician Beetle grows off every sacrifice by either player, which includes our own Reckless Lackey and Gingerbrute activations and our half of Accursed Marauder. Unlike Carrion Feeder it can block, so a few counters on it stop our one- and two-power attackers. Sacrificing Reckless Lackey for a card or Gingerbrute for life while the Beetle is on the battlefield hands them a counter, so do those while it is off the board or kill it first.
Shambling Ghast is their most-played removal effect against us. When it dies, whether blocking or sacrificed at instant speed to a free outlet, its -1/-1 kills any of our one-toughness creatures, including a Gingerbrute or Clockwork Percussionist carrying Inventor's Axe. The specific blowout to avoid: flashing the Axe onto a one-toughness creature while Ghast and a sacrifice outlet are both on their board. They sacrifice Ghast in response to the attach trigger, the target dies, and the Axe sits unattached while its pump misses the combat. With that board in front of you, put the Axe on Reckless Lackey or Goblin Tomb Raider instead.
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Out:
End the Festivities comes in because every creature card in their deck has one toughness, and so do their Squirrel, Insect, and Mercenary tokens. For one mana it kills everything they do not grow in response and deals 1 to them. Whatever they sacrifice to grow Carrion Feeder, Bloodthrone Vampire, or Mortician Beetle out of range still dies, and its token is already on the battlefield when the sweep resolves.
Searing Blaze comes in because sacrificing the targeted creature in response does not stop it: the damage to them still resolves. Even without landfall its 1 damage kills any of their unpumped creatures at instant speed, and on our turn after a land drop it deals 3 to a creature and 3 to them.
Cast into the Fire comes in to pick off two of their one-toughness creatures at instant speed, such as a Carrion Feeder and a Mortician Beetle before either has counters. Its other mode exiles Sylvok Lifestaff if they bring it in.
Goblin Bushwhacker goes out because against their 1/1 blockers its kicked +1/+0 changes no block: our one-toughness attackers still trade and our two-toughness ones already win. Many of those blockers leave tokens behind, so the all-out attack it sets up rarely finishes them, and unkicked it is a 1/1 without haste that, unlike the Voldaren Epicure we keep, does nothing when it enters.
Goldhound goes out because their board of 1/1s can usually spare two blockers for menace, so first strike takes down only one of them before it dies, and with no haste it adds nothing the turn it lands. Unlike Voldaren Epicure, whose ping and Blood token land whether or not it survives a block, all of Goldhound's value depends on combat.
Mirran Banesplitter goes out because its 
equip is the slowest way to move +2/+0 once Shambling Ghast, Tragic Slip, or a block kills the carrier, while Inventor's Axe re-equips with the energy it brings, so the equipment slots stay with the four Axes.
One Voldaren Epicure goes out because it is the only creature we keep with no haste, no first strike, and one toughness, so it is the cheapest trade for their 1/1s and Shambling Ghast's -1/-1. Three copies stay because the ping and Blood token still add damage and keep the artifact count up for Goblin Tomb Raider and Galvanic Blast.
Sideboarding moves this matchup moderately in their favor: our additions kill their one-toughness creatures but still leave behind the tokens those deaths create, while their lifegain and Drown in Sorrow hit both our life-total plan and our board at once.
Their lifegain and Drown in Sorrow make post-board games longer and punish overcommitting, so End the Festivities, Searing Blaze, and Cast into the Fire have to clear their one-toughness blockers while our burn still covers the life they gain back. Cast End the Festivities in the first main phase and attack right after: Nested Shambler's Squirrels come in tapped, so of the tokens the sweep leaves behind, only Insects and Mercenaries can block that turn. With Carrion Feeder or Bloodthrone Vampire out, they can sacrifice spare creatures in response to grow the outlet or Mortician Beetle out of range. Searing Blaze still deals its damage to them if they sacrifice its target, so cast it on our turn after a land drop for 3 to a creature and 3 to their face; on their turn its 1-damage mode still kills a fresh 1/1.
Expect Drown in Sorrow, extra Tragic Slip, and lifegain. Drown kills every creature we have, so once they have three mana, add only the bodies the clock needs and sandbag the rest. Sylvok Lifestaff, Vampiric Link, and Spinning Darkness all gain them life, so a burn finish has to cover what they can still gain. Cast into the Fire's artifact mode exiles Sylvok Lifestaff before it turns each equipped creature they sacrifice into 3 life. Gingerbrute carrying Inventor's Axe stays our hardest damage for them to stop in combat, since nothing in their deck can block it once its ability is used.