As mentioned in the comments, most of it is preference and opinion.
In practice, most of the actually quantifiable 'benefits' are dependent on how the hardware rescales the signal, and possibly on what other features the display might have.
If you take a regular 1080p signal, and just make each pixel of that signal represent a 2x2 block of 4 pixels when upscaling to 2160p, then there will be essentially no advantage in terms of resolution. If, however, you apply either some more complex matrix-convolution based upscaling algorithm (for example 2xSAI), or do some kind of anti-aliasing post-processing, then there may be some discernable difference in image quality relative to an identically sized 1080p display, though it will usually be an improvement in quality for certain types of images, and a degradation of quality for others (for example, the above mentioned 2xSAI is great at up-scaling pixel-art type images as found in old video games, but it makes text blurry, and it will absolutely murder photo-realistic images).
If possible, I would suggest testing each of the options under the conditions you think it will be used, and then picking the one that looks best. Most likely, you won't notice much difference between the three projectors unless they're from different manufacturers or are significantly different models, in which case just going with the 1080p should be fine (since it's probably the least expensive).
Just a few more tips:
Unless you are planning on mirroring or duplicating the laptop screen to the projector, you can ignore it's resolution for the purposes of this discussion. Short of really cheap stuff, all recent laptops should have good enough video cards to drive at least a 1440p (2k, or quad-720p, depending o who's marketing it) displays at native resolutions, and most decent ones will also be able to drive 2160p (4k) displays, even if the laptop itself doesn't have such a display. Note also that most laptops will not be explicitly advertised as 2k or 4k capable because connecting to an external display isn't a normal use case for a laptop.
Assuming your laptops really are just putting out a 1080p signal, the upscaling will be done by the projector, in which case the exact brand and model may have a very big difference on image quality. This is true of all displays, not just projectors (and there are a couple of brands of monitors I actively avoid for exactly this reason). As stated above, if at all possible, try the different options.
Stupid as this sounds, the cable you use can matter too. Usually, it will just limit what resolution you can run the display at, but some particularly cheap cables may give you visible interference in the image even at rated resolutions.
Most "advantages" will be based on preference and opinion. Scaling is normal and easily accomplished by most devices. HOW they scale may have some impact, but a native source will always result in a superior output. This question also falls quite close to a hardware shopping question for these reasons. – music2myear – 2018-04-10T18:36:34.550
Most sources are visitors computer which is why mostly fullHD is the maximum – Wayne – 2018-04-10T18:41:51.257