Being a long-time user of smaller-than-35mm cameras and enjoying their sharp and all-in-focus images in street photography, my early experiences –more accurately put, re-encounter, considering film era- with 35 mm format – was initially difficult. Shots were easily got out of focus. Lack of any visual indications (i.e. split screen or micro prism) in modern digital cameras added to the problem . I was being at the mercy of cameras autofocus system unless I use the more accurate, but usually difficult-to-use live view.
The larger area of 35mm format sensor – in comparison to smaller formats- increases the light capturing ability and improves the low light performance.  Larger pixels -if the sensor pixel density kept at reasonable levels- helps improve dynamic range. Also, rendition of out-of-focus areas can be softer using smaller f-number  These create enough motives to try to go up the ladder of sensor sizes to achieve better picture quality and creative control. But there’s a downside to this. As you opt for larger sensor sizes, controlling the focus and depth of field becomes more difficult. A tiny misplacement in focus point translates to visible softness. F-numbers considered safe in a Micro Four Thirds or APS-C formats, can have very shallow in-focus depth in 35mm. Get close to f/1.4 or smaller f-numbers and the in-focus plane becomes so thin that focusing accidentally on an eyelash can make subjects’ eye look slightly blurry.
Let’s look at an example: A typical APS-C Nikon camera with its kit lens at 18mm and f/3.6 focusing on a subject 3 meters away will have ~1.2 m in front and ~5.7 m behind of the subject in focus. That’s ~6.9m of in-focus depth, which leaves a very good safe margin in case several non-linear subjects needed to be in focus at the same time, for example, people standing in a U-shaped group.
Doing the same calculations with a full-frame Nikon with same f-number and angle of view  and the total in-focus depth reduces to ~3.2 m. Now you have less than a meter in front and about 2 meters behind the focus point in focus.
In some circumstances, the unforgiving nature of 35mm in comparison to smaller formats eliminates most of the probable advantages for choosing it in the first place. For keeping the subject in focus you need to choose a smaller f-number, losing light gathering advantage you had to some extent. You might need to bring more light into the scene to compensate and hence complicate the process. If you do all these and manage to keep your focus on the creative aspect of the work at the same time, you get better results than a smaller format. 
That’s why I envy the owners of latest APS-C cameras. If you begin purchasing a system nowadays, there’s a real opportunity to be very happy with APS-C and Micro Four Third systems nowadays. Everything is achievable with them except very low-light (like music photography in bars), For monochrome, photojournalistic work they are adequate and you enjoy a smaller system within budget. Camera’s are fast and have deep buffers, autofocus is accurate and minor mistakes in choosing the aperture are forgiven. For people like me, who really need 35mm (and larger) for certain type of jobs, it’s just more shooting discipline, awareness about the in-focus range and refusing the temptation of getting carried away by the allure of wider apertures.
After all, there’s so much wisdom in Arthur Fellig’s famous quote, when asked about his technique: “f/8 and be there”. 
 With a physical limit on the number of photons that a sensor can receive per exposure, each sensor size receives and records a finite number of photons per area. Obviously, the actual number of photons that their values are recorded with precision is less than the maximum theoretical limit, but even if theoretically ideal sensing device was achievable, able of recording 100 percent of photons it receives, still the data being sampled cannot exceed the total number of photons. So here’s where the size of the surface area becomes the key factor in sampling more photons in the same exposure timeframe and having more image information to work on.
 F-number is the ratio of the lens’s focal length to the diameter of the entrance pupil. F-number –being a ratio- is equal among cameras with difference sensor sizes, but it doesn’t mean physical aperture size and light gathering capability with the same f-number is equal among various formats.
 I understand why Fujifilm and Four-Third Consortium chose to build their system on a smaller format. They correctly anticipated that the technology will progress to the level that quality will be acceptable under most conditions and eventually will surpass and cover all typical shooting scenarios. Because they were early movers, the investment of the Four-Third standard consortium took a long time to show a positive return. Early camera’s low-light performance was subpar and contrast-detect AF was less capable than phase-detect systems used in DSLRs. Later, with better sensors, on-sensor phase detection, and better contrast-detect systems the gap narrowed. And they are not still 100 percent there. For Fujifilm however, the return of the benefits of this approach bears the fruit faster, because they have chosen a format only one step (and stop) behind the 35mm. Just look at the recent photo samples of the X-T2.