I had the software update for X but now I got Y. Is there any problem if I have them both?
There is no problem having both ds cartridges on the same system since both games are different. Either one will require an update via Nintendo E-shop (store). You should get diverted as you in-put the Pokemon Y game (it'll say an update is required) and gives you the option to go directly to the store.. Further info at this site..
Hope I helped