Curses are labeled as "curse" in the descriptive text and have text describing exactly how it interacts with the Remove Curse spell.
Monster Example:
Monster Manual page 229: A creature that takes treasure from the lair is cursed until the treasure is returned. The cursed target has
disadvantage on all saving throws. The curse lasts until removed by a
remove curse spell or other magic.
Item Example:
Dungeon Masters Guide page 152: Curse. This armor is cursed, a fact that is revealed only when an identify spell is cast on the armor
or you attune to it. Attuning to the armor curses you until you are
targeted by the remove curse spell or similar magic: removing the
armor fails to end the curse. While cursed you have vulnerability to
two of the three damage type associated with the armor (not the one to
which it grants resistance).
The most likely interpretation is that if an item states that it cannot be removed without remove curse, then it cannot be removed without remove curse.
Reason 1: Specific beats general
The principle of "specific beats general" is stated as follows in the Rules Compendium (2007):
A general rule is a basic gudeline, but a more specific rule takes precedence when applied to the same activity. For instance, a monster description is more specific than any general rule about monsters, so the description takes precedence.
While dispel magic in general can suppress magic items, specific cursed items can override this with specific properties.
Reason 2: Item descriptions
Cursed items are usually explicit when naming the spells which will counter their curse. For example, consider the Gauntlets of Fumbling (emphasis mine):
Once the curse is activated, the gloves can be removed only by means of a remove curse spell, a wish, or a miracle.
The item text is very specific: the item cannot be removed, except by one of the three named spells. It does not say what happens when you try any other method or spell, only that it will fail.
Note that this particular curse only prevents removing the item. It may still be possible to temporarily dispel a cursed item's other magical properties.
Reason 3: Primary source rule
According to the D&D 3.5 errata, when two rules come into conflict, the Dungeon Master Guide takes precedence over the other rulebooks when it comes to rules for magic items and cursed items, since the DMG is the primary source for those rules.
(However, this is not a watertight argument, since by the same token, the Player's Handbook is the primary source for rules on spells, such as dispel magic.)
Reason 4: Adjudication by similar rules
The Dungeon Master's Guide gives the following advice to DMs adjudicating ambiguous situations:
When you come upon a situation that the rules don't seem to cover, consider the following courses of action:
- Look to any similar situation that is covered in a rulebook. Try to extrapolate from what you see presented there and apply it to the current circumstance.
In other words, it's reasonable for a DM to interpret an ambiguous rule by inferring a solution from other related rules. The closest similar situations I can find are as follows:
- The spell bestow curse says that "the curse bestowed by this spell cannot be dispelled". This supports the idea that curses are specially resistant to dispel magic.
- The Loadstone, a cursed item, will return to your possession even if you destroy or throw it away. This suggests that even if you temporarily outsmart a cursed item, it will return.
Best Answer
Depends on the actual description
In true 5e fashion, you have to read the description of the individual item to know how it works. In the way of general rules we do get:
but that just highlights the existence of exceptions. Also, the rules on cursed items (also on DMG 138) do not say anything about their effect working differently in this regard, you are either attuned or not.
Let's see an example for both options. The description of the Berserker Axe states:
My interpretation is that this marks it as an exception to the rule, giving you the +1 bonus without attunement. There would be no need to add the part about attunement otherwise. However, there might be some debate about how explicit should the stating of such an exception be, and I recommend reading this answer for some perspective before you make up your mind about it.
The issue is much clearer in other cases, for example of the Dwarven Thrower:
There is no additional mention of attunement in the description, so the default rules for items with attuenment are in effect, making all properties tied to attunement, including the flat bonus.