BebuLamar wrote:
Does the Fuji have leaf shutter? I doubt that.
No, the Fuji does not have a leaf shutter.
To answer the OP's question, the mirror less cameras (which, as mentioned already, come in a spectrum of qualities) are a different tool, and definitely have their uses.
IQ is based on the sensor as well as the lens; it is said the reason the Nikon D800 produces a better image than Sony's FF camera (which uses the same sensor, manufactured by Sony) is that Nikon's engineers do a better job of interpolating the raw data off the chip. The Fuji cameras (and some others) have DX sized chips, quite comparable in quality to those found in DSLRs.
As for the glass; as with DSLR lenses, there is a range of quality - but the best lenses are certainly on par with DSLR lenses - at least for real-world use (those who take photos of brick walls and resolution charts need not apply). Due to the shorter distance from sensor to lens in mirror less designs (in order to make room for the mirror box, DSLRs have about a 40MM minimum distance from the lens flange to the chip) some lenses are easier to design, notably wide-angle lenses with focal lengths shorter than 40MM. The Zeiss and Fuji glass out there is quite excellent, and the other major brands are no couches, either.
As a tool to take photos - which is more suitable depends on the kinds of shooting you do. The EVF's ability to display the scene more-or-less as it will record can be a huge benefit for landscape work, for instance. When I put my 9 stop ND filter on my DSLR, I can no longer see through the viewfinder at all (frankly, I can't see through the damn thing when I hold it up to my eye in broad daylight) yet on my Fuji X-T1 the scene is there, easy to frame - quite astonishing the first time I saw that! And if I dial in +2 stops of exposure, the EVF display mimics that as well. Of course, it can't "show me" the blur caused if I have a shutter speed of 45 seconds, but compared to the old way of "compose shot on tripod without ND filter, mount filter, take shot, remove filter, find new composition, replace filter," etc etc ad nauseum using the Fuji is a godsend.
On the other hand, the EVF's ever-so-slight delay and the camera's lesser ability to focus in low light push me to use the DSLR for event shooting, particularly indoors. And while this comment inevitably elicits all kinds of foot-stomping denials from some folks who declare there is no difference, I am not the only one who has made the observation.
That all said, alluding to the quote attributed to the news photographer Weegee decades ago - "F8 and be there" - the (much) smaller mirror less kit can mean the difference between taking the camera and not having it at all - a mirror less with a pancake lens takes an infinitely better image than a smart phone, after all.
So, in the end, and to answer your specific question - "no, not for every situation". But the answer is assuredly "yes" for some things...it really depends on your interests.
Of course, as technology inevitably improves, the EVF issues will fade away and the greater simplicity of manufacturing mirror less cameras as compared to the mechanically oriented DSLRs will put the latter out to pasture at some point.