What are the main differences between aperture and ligthroom?
There is a sticky on that. You can find fanboys for both. Both are essentially a library manager with non-destructive editing tools. But IMHO neither has everything a photographer needs to develop every photo. That is why I spend more time on a given image in plugins (Nik, OneOne, PixelMator, Helicon), than I do in LR or Aperture.
No correcting lens distortions, no upright, and so on.
Correct. LR has some. But if you want serious lens corrections you need to get DXO Optics plugin. Again neither Aperture or LR can do what a specialty plugin can do.
I am just getting used to lightroom for ipad and i find it very limiting.
How is aperture on the ipad? Same as the mac version?
No Aperture lite for IOS at this time. I personally don't get trying to use such a resource limited (CPU, GPU, memory, screen size, missing keyboard and mouse, wacom connection?) device to do photo editing. In the field I use my rBBP screen for initial edits. At home I complete the work using an ATD. Both screens are calibrated.
It one thing for Adobe to release LR for iPad in the hopes of further binding folks to their cloud. It is another for Apple to do that as Aperture is not a cloud service (thank goodness).
With luck, at WWDC Apple will announce 4K support in 10.9.3 for rMBPs. And just maybe they will announce a new ATD that is 4K. And that would set the stage for a new Aperture that can take advantage of higher resolution screens. We have a month to wait for WWDC.