Comparing +1 to a stat to +2 to hit
Naively, the +2 to hit has obvious impacts on all characters, in most cases.
Situationally, the stat-bonus might be better, so let's break it how it effects a character.
Granting +1 to a stat has the following effects, if the stat is odd:
- +1 on ability checks associated with that stat (skill, initiative, or otherwise)
- +1 on hit rolls associated with that stat
- +1 on damage rolls associated with that stat
- +1 on saving throws associated with that stat
- +1 prepared spell, for clerics, druids, paladins, and wizards (assuming a bump to their spellcasting stat)
- adding 1' to high jumps (STR)
- +1 armor class, for some armors (DEX)
- +2 to max HP, as you say they'll be level 2 (CON)
- +1 minute breath-holding (CON)
No matter the parity of the stat granting a +1 will have the following effects:
Possibly opening up multiclassing opportunities (The "natural aptitude" language of the multiclassing rules makes the argument that preregs must be met by ability score distribution, racial modifiers, ASIs, and permanent magical increases (tomes, wishes, &c.) rather than by a magic item's temporary/ongoing boost.)
- Increasing running long jumps by 1', standing long jumps (broad jumps) by 1/2' (STR)
- adding 15# to carrying capacity (STR), 30# to push/drag capacity
- may open up new available choices for armor (STR)
(Note: I have ignored certain high-level traits, such as Indomitable Might or Visions of the Past which do key off of scores; they're beyond the scope of OP's players.)
Generously, we might assume that a character has a 50% chance of benefiting from effects in the first list. Multiclassing is a long-game issue, so I largely discount that impact. It's a rare table that tracks encumbrance, long jumps don't come up that often, and most characters are built out to already provide for their desired armor.
In short, the +1 stat increase likely provides little advantage in the short-term.[3.5]
+2 to hit is useful in almost every situation. True, some of your spellcasters may have good spells that focus on saves, rather than hit rolls. (That's good strategy, to have that choice when heading into combat!) But it's a rare character that can't benefit from a 10% increase in the probability that they'll hit.
All-told, this is a matter of playstyle.
I don't think there's a definitive way to answer "is +2 to hit better than +1 on a chosen stat." It may be possible to answer "is +2 to hit better than +1 STR for an unarmored half-orc barbarian wielding a greatclub who wants to hold down the front line and always go after the opponent's biggest target?"
In laying out the impacts of each above, I hope I've given you the tools/information necessary to gauge for yourself.
Do you need to adjust CR?
CR in 5e is not nearly a precise-enough measure that you should look at this to be your adjustment. +1 on a stat, even +2 to hit, isn't that large a difference that it overwhelms the single largest factor in how hard an encounter is: how you, the GM, play it.
First, the encounters in the early parts of HotDQ are known to be a little challenging. For your party they may be slightly less-so. Fine.
Second, much of the challenge of any encounter stems from how the battlefield is set and how the monsters make use of the situation wisely. Or don't. You're in charge of this lever, and it exerts much more influence on the encounter than does a potential +1 to a modifier. After all, if your ranged attackers enjoy half cover (PHB p.196, "Cover") that more than offsets the stat-bump.
Third, you control when characters level. Do they gain experience at the end of an encounter? End of a session? At the end of a "section" or "chapter"? Do they level immediately (as PHB p.15 "Beyond 1st Level" suggests), or require a long rest (as Adventurer's League does), or require training/downtime (as my table does)?
Fourth, even if they "over-level", they won't stay that way for long. The upward curvature of the Character Advancement table during the first tier-and-a-half ensures that.
 Your question asks about +2 to hit vs. +1 INT, but in order to consider the benefit compared to your other players we should consider all of the stats, not just INT.
 Certainly most players would be less likely to benefit thusly, as they've arranged the stats they care about to be even. But perhaps these players aren't as meta-gamey, or they rolled stats, or they're setting up for a level 4 feat and anticipating a +1 to their favored stat. In any case, I think 50% likelihood of benefiting is a good upper bound.
 And that's a shame, in my book.
[3.5] By "short-term" I'm talking about a few levels' worth of play, likely a half-dozen sessions. On the other hand, a character that'd intended to bump CON by two with their first Ability Score Increase can now choose the Durable feat; the character that'd intended +2 to STR can now choose Heavy Armor Master. Or Observant. Or Resilient. These provide interesting and impactful bonuses, if delayed a bit from the acquisition of the amulet.
 There's a slight deviation from this at the low end: if your THACX is 3 or lower, the +2 to hit either only helps you 5% or not at all!