As detailed by designer/publisher Brent Povis in this thread:
Very little has changed between the first and second edition. Here's the breakdown:
• Art: Only change is the art for the foraging stick punchboard tokens
• Gameplay: One minor rule change in which you now resolve a destroying angel dealt to you in your starting hand by discarding it (since you have fewer than 4 cards and no cooked sets) rather than holding it. I still play with the original "hold and deal with it" approach, but it's simpler and more consistent with the action of the card to do it the new way. Very minor in the grand scheme.
• Box: Same art, quality.
• Cards: Minor stock difference with the new manufacturer, but same art, quality, thickness, pliability.
• Instructions: Same with a few minor edits for clarity and the aforementioned DA rule.
• Love: Same.
While initially noting that the component tray was the same as in the first edition, Povis later clarified that:
There is some added clearance in the card wells over the 1st printing. Vertically there is 7mm clearance (3.5 on each of top and bottom if cards are perfectly centered in the well), horizontally there is 4mm clearance (2 on each of left and right...). I wasn't able to change the height, so depending on the thickness of the sleeves that dimension might test the top of the wells, but there is ample clearance between the top of the well and the inside of the box lid, so there's no concern about the box not fitting properly even if thicker sleeves do result in a few cards washing over the tops of the wells. I hope the sleeves will fit for you and that this helps.