Nowadays, there are a lot of smartphones which offer OIS in their camera. I wonder if there is any difference compared to the lenses in DSLR camera. And most DSLR lenses are rated 3-4 stop IS, how about smartphone camera? Is it just as effective as DSLR lenses?
You have to distinguish between software and hardware image stabilisation, often referred to OIS - Optical Image Stabilisation - for the hardware kind, where the lens or sensor moves to counteract camera shake and perhaps just IS for the software kind, where software techniques are used to remove the effect of shake. However, Canon's stabilised lenses have traditionally been simply labelled 'IS', despite being a hardware-based optically stabilised system implemented in their IS lenses.
There are 2 ways to implement IS in hardware - move the lens elements or move the sensor. With in-lens IS, every lens has to have the IS capability; with sensor based IS, the IS hardware is in the camera and benefits every lens fitted. As far as I am aware, all phone cameras that implement IS have sensor-based systems.
Software-based IS only works (I think) for video and attempts to identify a consistent part of the image and keep it aligned from frame-to-frame, cropping the image slightly. This can be done as the video is recorded or afterwords in video editing software. The former method required that the camera implements software IS; the latter doesn't.
Traditionally, stabilisation for D-SLRs has been lens based and was mainly seen on Canon (IS - Image Stabilisation) and Nikon (VR - Vibration Reduction) lenses. Now most lens manufactures offer stabilised lenses whilst body-based stabilisation is becoming more common, although not by Canon and Nikon, who stick with a lens-based solution.
Proper hardware based IS is just becoming more common in phones, and is exclusively sensor based, but the systems are largely equivalent.
On DSLR, using a stabilized wide-angle (including myself) is considered useful when shooting handheld in low-light situations. The subject should be rather static, otherwise subject motion blur will still occur during the longer exposure. Another small benefit would be stabilizing the "viewfinder" image on screen (and similarly, recorded video). Intended usage is the same on smartphones.
In a smartphone, operating principle is also the same as in DSLR - either lens elements or sensor is moved to counteract movement of the camera body. You are more likely to actually use stabilization in the situation described above, as the alternative solutions like tripods or external lighting rarely go with the ultra-mobile idea of smartphone photography; raising ISO is limited on tiny sensors. You'll also need stabilizing more often as the smartphone camera is much lighter, so it's more responsive to shaking hands. Camera position is less stable -instead of supporting head against the viewfinder it's held away from photographer by extended unsupported hands. More surface per weight also makes it more receptive to wind gusts.
Hard numbers on effectiveness are unfortunately hard to find yet. Lars Mark was satisfied with OIS of Google Nexus 6 allowing 1/2 second exposure and iPhone 6 Plus performance at 1/4 seconds. These exposures are 3-4 stops slower than would be expected by rule of thumb.
Rich W Woods has also tested image stabilization in iPhone 6 plus and found it useless. I suspect testing method being the main culprit of seeing no clear benefit. The apparent sunshine in the scene tells the scene was well lit to cope without stabilization, so the movements of the camera must have been larger than human hand-shaking that optical stabilization is designed to cope with. Similarly, Lance Ulanoff has found that OIS cameras perform only slightly better when capturing action on the move, but again, this is not what OIS is for.
There seem to be more satisfied reports though. Michael Fischer does give example photos of the benefit of stabilization on Google Nexus 5 for low-light situations, but doesn't provide any measurements of how many stops of difference the feature actually makes. Florence Ion considers OIS of Samsung Galaxy S6 "impressive".
Did you consider that smartphone cameras are usually much wider (lower apparent focal length) than dslr VR/IS lenses? Wide lense at f<50mm will not benefit from stabilization, because linear distance of image movement is much smaller than with something like f=200mm on FX for same camera tilt caused by of hand tremor.
Also VR might help to alleviate shakiness due to mirror flipping, as Nikon mentions.
So, in my opinion, comparing smartphones' cameras with DSLRs, and what major (canon is similar to nikon) manufacturers of (D)SLRs do with VR, OIS in phones is just an additional feature to drag more buyers. Like more smaller pixels for higher price with higher noise level (smaller pixel = more noise).