You seem to be unaware that the slayer's damage bonus with all weapon attacks ramps up at a similar pace as the rogue, topping out at 8+Dex mod--or at least, you don't account for it. Advantage=Slayer
Likewise, the rogue's +1 to hit with certain weapons is trumped by the slayer's +1 to hit with all weapons. Advantage=Slayer
8+Dex mod does not trump 5d6+5, let alone 5d8+5. Assuming a huge focus on Dex, which is a secondary stat for Slayers, you're still getting only about +16 to the attack, and concidering the fact that Thieves get brutal sneak attack damage, the minimum extra a thief will get is +15. And the Thief doesn't need +1 to all weapons because they only need to use Thief weapon types.
Felon said:
As stated before, the slayer's stances tend to be more generous than the thief's in regards to attack and damage bonuses. The thief can get +2 damage under certain conditions, while the slayer can get a conditional +4, and has a completely unconditional +2 damage stance to fall back on. Advantage=Slayer
Thieves get +6 to damage rolls with Acrobat's trick, unconditional. Also note that the Thief's tricks are about being mobile not additional damage. So again, Slayer doesn't trump Thief.
Felon said:
You bring up feats like backstabber and light blade expertise. Slayers get feats too. Once again, you're emphasizing what the thief gets and overlooking what the slayer has access to.
Alright, a Slayer is likely going to take either Heavy Blade, or Axe expertise, giving them a +2 bonus to Defenses against OA's, or the ability to Reroll one damage die that Results in a 1 but must use the second result. But then if a Slayer wants to use an Executioners axe, Axe Expertise has no benefit for them, so most likely a Slayer will wind up taking Master of Arms. You bring up Slayer's having higher AC then Thieves, which sadly is also unlikely. A rogue uses Dexterity as their main stat, which benefits them greatly to have high, and so assuming both classes take the ideal armors for them, will either have a Slayer in Scale and Thief in leather for no feat cost, or a Slayer in Plate and Thief in Hide for one feat. So a slayer is going to have either a +13/14 from their armor, while a thief will have +14/15. Even more to the point, a Thief uses one handed weapons, allowing them to have a parrying dagger in their off hand and benefit from Two Weapon Fighting and Two Weapon Defense, increasing their AC and damage even further. Now a fighter is able to take Power Attack to increase their damage, but at the cost of accuracy, which tilts things even more in favor of the the thief.
Felon said:
So at the end of the day, the thief is counting on sneak attack to catch up to and, hopefully, overcome the slayer's lead granted by superlative two-handed weapon and larger static bonuses. And while that might happen at 21st level when sneak gets an abrupt 2d jump, that's cold comfort to someone starting at 1st.
"Quite easy?" Not quite.
Having said all that, the point that really got missed was that giving the rogue bonuses when using sneaky weapons is a far better mechanic than locking them down to a specific weapon group.
Yes, a Slayer may do more damage at level 1 due to using a larger damage die weapon, but frankly? Not by much. A rogue will be doing a minimum of 4 damage extra at level 1 with finesse and sneak attack, where as a Slayer would need 18 dex to do as much extra damage, which for a secondary stat is expensive so more then likely the Slayer will be doing 2-3 extra damage, which balances the difference between weapon die imho especially seeing as the rogue is capable of doing a total of 14 extra damage nearly as much as the epic Slayers bonus damage. So yes, a thief is quite easily able to out damage the slayer, as well as being highly mobile and of more use out of combat thanks to their skills.