I have my concerns about a Druid being better thief than a Rogue of the same level. As a DM, should I prevent using the Wild Shape as a high-end burglary tool, and how?
The Wild Shape feature has no restrictions for an animal size, which makes this feature quite tempting for any rogue, from my understanding.
Starting at 2nd level, you can use your action to magically assume the shape of a beast that you have seen before. You can use this feature twice. You regain expended uses when you finish a short or Long Rest.
Your druid level determines the Beasts you can transform into, as shown in the Beast Shapes table. At 2nd level, for example, you can transform into any beast that has a Challenge rating of 1/4 or lower that doesn't have a flying or swimming speed.
PHB gives examples of turning into wolves, crocodiles and eagles. But really overpowered is turning into a very small animals, like spiders or mice:
The greatest thief
At 2nd level, the Druid becomes an ultimate escape artist and completely overshadows the Rogue:
Infiltrate a heavily guarded territory. Forget Stealth checks, making a disguise or bribing guards. Just turn into a little mouse and go through the main entrance. Or you can turn into a spider and climb walls unnoticed.
Pass a reinforced locked door. Again, turn into a spider and climb through a keyhole or under the door. Since all the equipment can be merged into a Wild Shape, you can take your loot with you.
Hide in an empty room. Enemies are about to find you, but you don't know the Invisibility spell? Turn into a mouse! Besides from Stealth checks advantage you will get Total Cover even behind the smallest objects. Or you can turn into (again!) a little spider and just sit on a ceiling.
A ghost that leaves no traces. Pass traps, walk on pressure plates…
Escape from any ropes and chains. Being chained into manacles, you don't need to make DC 20 STR or DEX check. Just turn into a mouse.
Escape from a prison. There are plenty of rats in prisons and dungeons. Turn into one, slip through the cell bars and be free.
As a DM, how can I limit the Wild Shape feature, to make the Rogue on par with the Druid?
Best Answer
You got the basic rules right. See also this linked question, there is no lower limit to the size.
So, let's move on to the second question: why isn't it overpowered?
Let's go over your ideas, and see what we get.
Escape from any ropes and chains.
Yep, totally feasible. The advantage here is that you can escape in a single Action, whereas it takes the Rogue a minute or so to fumble out of their bonds; hardly game-breaking, especially given that you have to spend one of your two Wildshapes to do it.
If you are alone, then the Rogue would've also escaped without spending a limited resource. If you are not alone, you are now stuck in a mouse-form and about to get stomped on, with excess damage going into your druid shape, and you'll need your next Action just to turn into something more dangerous to fight. It's quite expensive for a not very powerful use.
Escape from a prison.
There are a lot of things in a prison that are dangerous to rats, including other rats, cats, careless guards, and other vermin hanging around the place. You'll need to stick to your rat-form until you are outside, which might take a while for bigger dungeons and because you'll be navigating unfamiliar territory. Don't expect this to be in any way easy. Also, this assumes you're locked in a dungeon that doesn't have a solid iron door and all the rat-holes filled up; ie a low-powered dungeon that any other hero would probably also be able to escape. It's pretty easy to stop Druid-rat from getting out if this is supposed to be a dungeon that contains magic-users.
Infiltrate an enemy fortress.
This has the same problems as the above. There are a lot of things in a fortress that are dangerous to spiders, and if any of them deal even a single point of damage, you are now a Druid in their natural form in the middle of an enemy fortress with no way to escape. This is a very, very risky thing to attempt unless your Druid is naturally good at this stuff, because you will end up losing your Wildshape during this excercise.
(Also, hiding in someone's pocket requires a willing accomplice. If you have those, you'll probably have a good way to get in anyway)
Pass every door.
Great. What about your party? Unless the only goal is to retrieve a single item directly behind the door, this is likely going to be very dangerous again, because you'll be behind that door alone. If you do want to just retrieve an item, you'll need to transform back into a Druid, add the item to your equipment, and then transform into a Spider again, using both Wildshape attempts to bypass one door. Not very powerful.
The Rogue can probably get the door open pretty quickly, without spending resources. The Wizard can use a 2nd level Knock spell to open the door.
Hide in an empty room.
This is replicating a 2nd level invisibility spell and assumes whatever is following you is both unaware that you can do this and not the kind of things that would eat a mouse just because. Using a Wildshape attempt to roughly replicate a 2nd level spell isn't very powerful.
Increase your weight or drop it to almost zero.
The Levitate spell (also 2nd level) can do pretty much the same thing; this is a very niche application of Wildshape. These things come up almost never.
Conclusion
Wild Shape is certainly versatile, and can be used to do a lot of cool things. But it costs resources, most applications are an adventure in themselves (which is awesome, of course) and they usually work best if you're alone.
It's not overly powerful, but really versatile. Turning into all Nature's children to leverage their strengths (while also accepting their weaknesses) is your thing. You're good at it, just like everyone is good at something. But most Spellcasters can replicate what you do with some basic spells, and most Rogues can replicate what you do with a bit of time or a good die-roll. They just do it their own way.