I've seen them both and I've been tracking Entei because I want him for my team, but as luck would have it, I caught Raikou first! I didn't check the nature since I don't really care about those things, but for those who are concerned about them and haven't heard about it yet: If you faint Entei and Raikou, they will come back after you defeat the Elite Four (and they will have different natures). I used a Fast Ball to capture Raikou, but it took me a while. I just restarted every time it ran away until it showed up in my area again. It's the fastest way, I think.
Alannya, if you have a Gastly, you can use Mean Look and it will fight you. You will have a 3/4 chance that it won't use Roar so you can lower its health and put it to sleep or paralyze it, that is, if your Gastly is strong enough to withstand its attacks.
Since my Pokemon are only above level 25, I only had one chance to damage them each time they appeared until they finally had low health and were either asleep or paralyzed. And since I wasn't thinking, I made my Haunter forget Mean Look so I had to get a low level Gastly to Mean Look the two beasts while I just tossed balls until they Roared and fled or KO'd my Gastly.