This is what I like to call "an OK card."
It's not great when compared to the many ways to collect resources these days, but I don't think it's bad. As with most cards, this really only shines in two circumstances.
Quick recap for those of you who haven't scrolled down to CaiusDrewart's excellent review: this card is not as efficient as it seems. While it might seem like 3 resources for 1 action, you gotta do a little more math to break down the cost. The first action of playing actually nets you nothing. Strict loss for 1 action. You lose 1 action, 1 resource, and 1 card. After that, you spend 1 action for what I'd hope is a decent shot at 3 resources.
Scenario 1:
Play Burglary: -1 action, -1 resource, -1 card
Successfully Burgle: -1 action, +3 resources (if you are lucky enough)
Net change: -2 actions, +2 resources, -1 card
Scenario 2:
Get a resource: -1 action, +1 resource (guaranteed)
Get a resource: -1 action, +1 resource (guaranteed)
Net change: -2 actions, +2 resources
Obviously, this is a bad deal. In the first turn you've played it, you've only lost one card IF YOU ARE LUCKY and passed the investigate. However, this does recoup it's investment the more you use it. One more action (and successful investigation) and you've hit the same efficiency as getting two resources and playing emergency cache level 0. After that, it starts improving, but you're always hit with the possibility of failure. It's valuable if you can dedicate many actions to earning resources and you have an efficient outlet for those resources.
So, in most cases, it's bad.
But when is it good?
As has been discussed before, Rex is the gold standard. While in many situations, Rex needs to be a clue hoover spending each action getting as many clues as possible, there are a number of situations where Rex only has 1 clue at a location, whether you're playing solo or not. In these situations, it could be more efficient to burgle, get the resources and the clue in one fell swoop. In addition, with the ability of certain cards to move Rex between locations DURING an investigate (Shortcut level 2 and Pathfinder,) he can burgle a low shroud location with no clues, move to another location, succeed on the investigation, and collect his bonus clue from a new location (one that may be at much high shroud value.) There is math that could be done on the likelihood in each scenario you'll run into location with only 1 clue. The short answer is "it's pretty likely."
The second case is worth considering is the combo of Burglary with Lola Santiago. If the Rex combo is the gold standard, consider this the bronze minimum qualifications.
Lola's first aspect gives you that nice +1 to intellect and agility, which makes us better investigators. But it's the second aspect that really makes things interesting. Lola's fast exhaust allows us to convert resources to clues at a varying levels of efficiency. What this does is improve the value of a resource.
Suddenly, a single resource can become clue on 1 shroud locations. If a Rogue burgles a 1 shroud location and then uses Lola, they can net 1 clue and 2 resources for 1 action. On a 2 shroud location, the efficiency become 1 clue and 1 resource for 1 action, which is as efficient as Dr. Milan Christopher. That's ignoring the possibilities of burgling from a neighboring location and then moving to acquire a clue.
That said, the only aspect about Lola that makes Burglary directly more efficient is that +1 intellect, which can be accomplished otherwise. However, because resources are now slightly more valuable in terms of action economy, having an efficient way to consistently collect more resources throughout a scenario becomes more valuable.
Does that mean that Burglary is now good?
Nope. But it is adequate. The more and more we use Burglary in a given scenario, the closer our efficiency rating reaches 3 resources/action. It never quite reaches it because our first action cost 1 resource and 1 action, also because there is always a chance of failure. Over a single scenario, over 10 turns, we reach an efficiency of about 2.63, which drops to about 2 if we assume you only succeed 3/4 of the time.
Are there more efficient generators of resources? Absolutely, but few that are as beneficial over the length of a game and nothing is as card efficient. If you can pull off a Double or Nothing + Watch This combo, you get 9 resources for 0/1 actions and 2 cards. Hot Streak level 2 nets you 5 resources for 1 action and 1 card.
This card essentially gives you the fuel to repeatedly rely on Lola throughout a scenario. As you level up, you can supplement it or swap it out with Hot Streak or whatever else is more efficient.