That's a pretty broad question you asked. You'll have to narrow it down a bit more if you want a clear answer. Sorry.
No, in Diamond and Pearl you can't catch the legendary birds.
Not much. Pokemon diamond and Pokemon pearl have different Pokemon. for example, in pearl you can catch a glameow but not a cranidos and in diamond you can catch a cranidos but not a gleameow. And at the end of pearl you can catch Palkia the legendary and at the end of Diamond you can catch Diagla. But the games are basically the same. And there you go.....
you have to catch Palkia(in pearl)orDialga(in diamond)
You'll have to have received it from a special event.
catch palkia (pearl) catch dialga (diamond)
you have to catch it and then you you have to trade from sapphire or ruby or emerald to diamond or pearl
You cannot catch the legendary dogs in Diamond or Pearl, you must migrate from Pokemon LeafGreen, FireRed, Colosseum, or XD.
neither of them is better, they are both the same, but in diamond, you catch dialga, and in pearl, you catch palkia, and you can catch different Pokemon in each game for example: you can catch this Pokemon in diamond, but not pearl but: you can catch this different Pokemon in pearl, but not diamond
The only way to get the Legendary Beasts in Pokemon Pearl is to find them in FireRed, LeafGreen, HeartGold or SoulSilver, catch them and then migrate them over to Diamond via Pal Park.
Tornadus, Landorous, Reshiram, Virizion, Terrakion, Cobalion, Kyurem, and Victini.
You cannot catch palkia in diamond and dialga in pearl but you can catch both of them in Pokemon platinum
the legendary Pokemon you can catch in pkm d/p is dialga (diamond), palkia (pearl), cresselia, regigigas, heatran, arceus (event pkm), darkrai (event pkm), shaymin (event pkm) , azelf, uxie, mesprit. and giratina