I’m buying a car this Thursday and I’m stuck between these two cars.

-Mazda has 58k miles on it and it’s selling at $17,600

-Subaru has 53k miles on it and is selling at $15,800

I really value reliability on a car more than anything. Their fuel economy is identical. Which one should I go with??

I'd go with Subaru over mazda...but this is a Subaru forum so let's give some reasons.  I don't think Mazda's are top rated longevity monsters, though I'm not saying they're terrible. But I don't think those early year 2013 Crosstek's with first year CVT and FB's are the cream of the crop. 

How confident are you maintaining or being involved in any future repairs with Mazda or Subaru?  If you're more experienced on one manufacturer, or your favorite shop is, you might lean that direction.  For instance, all else being equal I'd favor the Crosstek simply because I know Subaru's so much better than Mazda's and think I can navigate online Subaru forums better (they're excellent).  Even if I didn't work on that vehicle I'd be much more comfortable talking to dealerships and have a wealth of friends/acquaintances to ask questions.  Support (info, repair, maintenance, shop familiarity, local dealer trust worthiness) is key in relaibilty too.  

I think I favor the financial aspect the most here:  Looks like you're getting a roughly $2k better deal for being a year older on the Crosstek.  That age difference is meaningless and the crosstek will probably retain it's value better over time like the Baja because they're so distinctive.  

I'd almost pull the trigger on the Crosstek for those two reasons alone - consider that $2,000 savings a repair fund for any future surprises, and also the distinctive value retention of the Crosstek.  

In more general terms, here's what I would do (and have done  I'm probably approaching 100 vehicles I've bought or helped people buy):

1. If you're in a rust prone area that's old enough to start incurring issues - I'd check all rear exhaust flanges, muffler welds/seams, hanger welds, and see if surface, or other, rust is starting. That's usually where it starts to show.   I'd let the rust be a major factor if: A. everything else seems equal, B. you live in an area with rust issues.

2. I've had good luck calling (or visiting) 2-3 Subaru dealers service departments in the home zipcode of the vehicle (you can usually figure out where it resided prior to sale by searching the VIN) and ask for the service records.  I've had them print it all out and hand it to me before with on questions asked.  Granted I've got some practice working with people and Subaru's and dealerships so that probably helps with comfort/success rates. 

To bad you can't add Subaru's 120k/120 month warranty onto that crosstek, that would be sweet.... 

2013 Crossteks have extended Subaru factory warranties to 10 years 100,000 miles for the CVT and oil consumption issues. 

So the Crosstek should have 1-2 years of factory warranty left on the engine and CVT.  Or it could potentially already have a new engine and CVT from Subaru in it. 

I would double check that that year Crosstek qualifies for those two extended warranties, and that my 10 year/100k is correct, I'm working off memory. 

As soon as you get the car - start using heavier weight oil - 5w-30 or 10w-30 and not that 0W stuff.  And change the CVT fluid immediately.  Subaru says "lifetime fluid" but that's nonsensical.

If you're intent on retaining documentation and that 100k warranty then i'd stick to Subaru's recommend oil viscosity of 0W or whatever it specifies until the warrant runs out.  Although I wouldn't do that, but that's a more wise one-size-fits-all solution for the masses. 

2013 Crosstreks have oil consumptions issues. With that low a mileage I would assume thats the case with this one. Make sure its been addressed before buying