Item rarity is unfortunately often simply inconsistent

Mark Wells' answer relating to the attenement cost of the Cloak is reasonable, however, there is another explanation for this apparent anomaly - it's an oversight.

Item rarity classifications are unfortunately pretty notoriously inconsistent. There are lots of examples of low level items that really punch above their weight and high level items that turn out to be pretty damp squibs.

As an example of this in practice, consider the relative rarities of the DMG items that provide a PC with the ability to fly:

There are a few items which give the ability to fly in the 5e DMG. Among the first I came across were the Winged Boots and the Broom of Flying. The Boots give a fly speed equal to your walking speed for 4 hours per day divisible into 1 minute chunks while the broom gives you a flat 50 foot fly speed all day long, decreasing to 30 feet if you are particularly heavy. Both are clearly very powerful, if you've got two sides in a combat one of which can fly and one of which can't the flying side has a huge advantage. If the other side also has no good ranged attacks the flying team more or less wins automatically. Yet both the Boots and the Broom are uncommon, they only cost 500 gold, pretty much any adventurer who decides they want one should be able to get their hands on one if they really want to.

Right under the Winged Boots are the Wings of Flying. The Wings give you a fly speed of 60 feet for one hour but then require a 1d12 hour cooldown period after each use before they can be activated again. Again, a pretty powerful item, but probably less useful than either the Broom or the Boots for most practical purposes. The higher move speed will occasionally pay off, but usually the ability to fly whenever you want will win out in terms of practical utility. At most, it's definitely not better than either the Broom or the Boots. The Wings of Flying are a rare item. They are worth 5,000 gold, 10 times what the boots or broom are worth.

The next item I found was the boots of levitation. These boots let you use levitate as the spell at will. Levitate moves you straight up or down only. It can never move you more than 20 feet off the ground or more than 20 feet up or down at a time. It has a similar weight limit to the Broom. It consumes your Concentration slot. You can't use it for longer than 10 minutes on end without returning to the ground. The boots of levitation are rare items. They are worth 5,000 gold, just like the Wings of Flying. 10 times more than the Winged Boots or the Broom.

The next item I found was the potion of flying. The potion of flying gives a fly speed equal to your walk speed the same as the Winged Boots do. It lasts one hour like the Wings of Flying, and can only be used once ever. The potion of flying is very rare. It is worth 50,000. 100 times what an item that gives precisely the same effect 4 times every single day forever does.
Saidoro, Sane Magic Item Prices (Emphasis mine)

So, it's possible that an uncommon item could be better than a rare one, what should you do about it?

Just think carefully about how any item that you plan to give your players might unbalance your game.

If you've already given your players an item that you now worry is too strong then there are a number of other questions on here that deal with ways you might be able to rectify that situation.

Practially, however, there's a reason that this fan-made list of Sane Magic Item Prices has become so popular - it corrects what many see as an obvious deficiency within the game. Before you give your players an item, why not check its relative value on this list and see how it compares to other items, either of its rarity, or that produce similar effects - you might find that doing so saves you from making a potentially costly mistake (it's not infallible but it's saved me a couple of times).

Relevant to your exact question - this pricing system puts the value of the +1 armour at 1,500 gp (in the middle of the rare item range you quoted from the DMG) but suggests that the cloak should be priced at closer to 3,500 gp (well above what the DMG suggests for uncommon items).