Dialga will have a 20 point decrease in it's Attack while getting a 20 point increase in it's Special Defense. In addition, it's signature move Roar of Time will be slightly altered. More specifically, it's power increases while it's accuracy decreases. It also increases the chance of going fewer times in battle, so use it with caution.
Palkia will have a similar 20 point loss in it's Attack while getting a 20 point gain in it's Speed. Palkia's signature move, Spatial Rend, also changes slightly. The power and accuracy of the move are both decreased, but in exchange, its chance of landing a critical hit increases from a +1 modifier to a +2 modifier, meaning that you will be landing critical hits even more than normal. (The boosted critical hit rate increases even more when using Spatial Rend in Strong Style, becoming +2 for normal Palkia and +3 for Origin Palkia)