Don't worry. I do not have the least inclination to argue that either is somehow wrong. On the contrary, both rate extremely high on my scale of "good things"™. People who adopt and/or donate their gametes rank equally high on my top list of "people to admire"™.
So, what are these dilemmas then?
Let me first address the one relating to adoption. I will assume we're only talking about adopting a really small child, one that is guaranteed not to have any knowledge or memories of its biological parents. As you'll see this is, in fact, a prerequisite for having this dilemma in the first place.
Let's now turn to the dilemma itself: should the adoptee ever learn who the biological parents are? If they ask, should they be told? Also, should they even be told they have been adopted, in the first place.
Not having been adopted myself I cannot speak from personal experience about the need to know one's biological parents. I believe I know who mine are, and thus cannot even simulate the wish to know properly. The best I can do is close my eyes and imagine I have, in fact, been adopted, but was never told. The first question would be: if I have such doubts, do I confront my parents? In the normal course of events parents shouldn't ever have the need to reassure their children that they are not adopted, so there may be a need to ask if you're in any doubt. My gut feeling here is: if you are in doubt, ask. Simple as that.
This leads us to the next part of the dillema: supposing you're told you're adopted. It doesn't really matter if you asked, or your parents volunteered the information. What do you do with this information now? Do you go asking and/or investigating who your biological parents are? If yes, why? If not, why not? I can again only go by my gut feeling, having closed my eyes and tried to imagine the situation. Having done all that, and opened my eyes again so I can type this, here is what I think:
If I was in this situation, and my parents have been as good to me as I can imagine (as for example my real ones have been) then I think I may not be very interested in the biological ones. If I also learned I was given up for adoption then I think I'd probably actively refuse to know. Why would I have a need for those who didn't need me? If I was adopted because my original parents perished when I was only little, then I would probably want to learn about them, but them not being around any more, that intereset, just like the knowledge would only ever be theoretical, so to speak. So, on balance, and having had a happy childhood I think I'd feel little need to burden myself with this sort of knowledge. Thinking about it, even if I had a terrible childhood I doubt knowing who my biological parents were would help in any way. It's unlikely that they'd take me back even I found them, and they were still alive. Why would they, having given up on me once already?
So, in conclusion, while if the question is asked it certainly has to be answered, and truthfully, I do not think knowing the answer benefits the adopted child in any signinficant way. Of course, if you're an adopted child, and feel I'm talking bull here, I'll happily admit I'm wrong. In your case. I'm talking probabilities here. Have a look here.
But this was really just an overture, covering the bases, if you want, before my main piece. And that is the right to know in cases of donated eggs/sperm. Not only is this something I can more easily relate to, but it's also something that has been a more contentious issue in public, too.
While I have not donated sperm, I think it is very easy for me to imagine that I had, and look for possible consequences. For the child produced from a donated gamete the dillema of an adoptee is applicable almost in its entirety. The difference is that parents giving up a child that has already been born are doing something completely different to someone charitably helping someone unable to have one. Do note, I equate egg/sperm donation and surrogat motherhood, and I also do not distinguish between possible ways of using donated sperm (think in vitro, and by traditional sexual intercourse). For the purposes of this discussion, and in my mind, too, they are all one and the same. Even if money changes hands.
So, assuming the child is told they've been created using donated gamete, and assuming it expresses the wish to know who the biological parent(s) were, does it have the right to know? My argument above was that an adoptee does. But I am not so sure about the child who has been conceived using donated gamete(s). Why is that?
Well, for one, the biological parents in these two cases are not really doign the same thing, are they. The ones who are giving a child up for adoption are presumably doing it after having a change of heart (unless they're dead, but that's a different matter altogether), while the donors are doing a good deed, presumably wishing to remain anonymous. After all, you do not really want to have every single child in Africa know that they're benefiting from your charitable donation. If you do, I'd say you're giving to charity for all the wrong reasons.
So the question really becomes: does a childs right to know trumps donor's right, and wish for, anonymity. Of course, if the donor is happy for their identity to be revealed then there is no issue here at all. And I also think the donor in this case cannot demand to be revealed to a child that hasn't asked for the knowledge of its biological parents in the first place. Which leaves us with the child who did ask, faced with the donor who wants to be anonymous.
Here, I must say, I will have to side with the donor. His, or hers, right to anonymity trumps the childs right to know every time. Even if the donor dies. It is a bit difficult, if not impossible, to clearly explain why, but all my being is telling me this is the right way around. You could say that the child owes it's existence to the magnanimity of the donor, and should not ask fro things the donor may deem ungrateful. It is true the child didn't ask to be born in the first place, but then that doesn't prevent it from having all sorts of other obligations it will not think of avoding. Not having asked to be born has never stood in court as any sort of defence, after all.
Another argument is that, if they have requested anonymity, it can be presumed that donors would not have donated at all had anonymity not been an option. And without donors there wouldn't be any chance for some people to have kids, so donors surely are a good thing, and something to try and not lose?
Unfortunately, this is something British law recently got wrong. Strangely, donor numbers have been reported as rising since, leading me to question donors' motives (it could also be that the numbers picked up from a dismal low becasue of increased publicity). The new law does not leave any choice to donors, as far as I see. You donate, you will be outed should the child so desire. Pity. The least that should have been done, rather than deny any anonymity, was to make anonymity an opt-in choice. If you ask for it, you get it. If you don't care to ask for it, you're fair game. And then also allow recipients to choose if they want to use a donor that requires anonymity. My preferred option would be opt-out anonymity, i.e. you're anonymous by default, but can ask for it to be waived.
Now, I am too old to donate sperm myself, but trust me, without guaranteed anonymity I wouldn't be interested anyway. At least in this there is no dilemma for me!