If you are going to lease and not purchase it's a matter of what will give you the best deal. IMHO, the biggest difference between Hyundai and Kia is the thin sheet metal used in Kias. They don't hold up in crashes or to shopping carts. The Kia should be less expensive and they often have better lease terms. The Santa Fe is very quiet inside the cab although leg room can get cramped for tall people.
They're both built at the same U.S. plant so the quality in workmanship is equal. There are a few differences, including the exterior appearance, but many of the parts are shared, including the platform. I prefer the appearance of the Santa Fe over the Sorento.
I have test driven the 2016 Santa Fe Sport 2.0 AWD Turbo w/Ultimate vs. the 2016 Kia Sorento SXL AWD Turbo.
The Sorento is a little bit quieter than the Sport (I used a sound meter and drove the same route). I believe the Santa Fe Sport topped out around 77 db and the Sorento around 75 db. Sorento has a much noticeably smoother ride (I didn't have my g-force meter at the time, so I can't tell you objectively what the difference in numbers were).
IMO, the Santa Fe Sport has better Turbo response (didn't notice turbo lag). I did notice turbo lag on the Sorento.
My main purpose of my initial test drives (also compared the 2016 Ford Edge SEL, although I'm looking at the Titanium, but nobody had any) was strictly to compare noise/ride levels. Due to none of the vehicles having Android Auto and/or Carplay, I put my car shopping on hold until this November.
Since then Ford has come out with the 2016 Edge with Sync 3 (AA/Carplay coming in an update by Ford). I have not test driven a 2016 model yet. Plus the 2015 model year from Ford was a complete re-design and had some QA issues (water leaking, etc.) However, it had the quietest/smoothest ride of all.
Hyundai has obviously released their 2017 Santa Fe Sport (and possibly the regular Santa Fe). They've added additional features and Android auto (I can't find squat on Carplay if it's going to be added or not). I have NOT test driven the 2017 model. My roomate has a 2014 Santa Fe Sport (non Turbo) which I like. However, the lack of power (I have a 2005 chevy Equinox AWD LT POS V6) is why I'm going/wanting the Turbo. I do not like the tightened suspension that Hyundai did in 2015 model year. I find the ride to be very stiff (much like a Toyota). I'd rather not feel every bump/pothole on the road (and where I live we have lots of them).
Unfortunately Kia has introduced (or announced) their 2017 Sorento and they are getting rid of the SXL Turbo trim. I do not want a 3rd row seat and the V6 model has crap for gas mileage (17 mpg, really? My POS Chevy that's 12 years old gets almost 19 city). The EX Turbo trim lacks most of the features I want, so Kia is out, unfortunately.
But I'm not sure if you want the Santa Fe vs. Sport (some people want the bigger vehicle with the third row seat, I don't).