I just did some repairs in my house (I want to sell it and it will help). Before I always took a water-based primer because I then tought that the alkyd one would prevent me to paint with latex over it. Well, I was wrong, you can put either latex or alkyd over it. I have learned and experienced that an alkyde primer is much better than a water-based one. It has a better grip on the wall and have less chance to do bubbles as it happened to me with water-based primer. And when THAT happen you are less than happy becaure you must redo the sanding and prep all over. Not funny at all. I can tell you that never again I will use a water-based.
I bought Prime Time, reasonnable price and very good adherence.
The only brawbackd I can think of is that you have to wash your brush with thinner. It doesn't smell good. But that's minor.