I thank you all for your input.
I believe that the decision is very close, and depends upon how you think your opponent will play. For example, if you do put your opponent on 88-JJ and you think he will fold on and over card or diamond, then it can be demonstrated that raising is superior to calling. I have even done and analysis of this in cardrunners ev as follows.
Suppose villain has 88-JJ and pots the flop. We make the following assumptions about how he will play the turn if we call: If the flush hits and he has an overpair with a flushdraw he will put the money in on the turn. If the flush does not hit and he has an overpair on the turn still he will put the money in on the turn. In all other turn spots he will check, we will bet every time, and he will fold.
I have input this into cardrunners ev and ran the equilibrium solver with this constraint. In that situation, the result is that calling is +EV of 11.88 big blinds. Basically villain will want to put the money in on the turn 57% of the time, in which case we will have to fold almost 90% of the time.
Now if we simply go all in on the flop and villain always calls, we have a +EV of 14.21 big blinds.
I have also assumed that there is exactly 16 big blinds in the pot going to the flop and that we exactly 100bbs deep preflop.
I will post the file on request for anyone who is interested.
Of course if you assume the opponent will play much worse in various imaginative ways on the turn when you call the flop, you can put almost anything into crev to make your numbers come up the way you want them too, for example if you get rid of the key idea that your opponent really doesn't like a flush card and will try to fold on that.
Now if you assume that your opponent does indeed have sets on the flop along with these overpairs it's undeniable that calling is better, but I really do not expect this.