I think you need to explain what you're interested in better. Are you particularly wanting to fly partners rather than the home airline, or do you simply mean you want to include partner availability? (One airline may have worse partner availability but better own-plane availability, and another vice versa.)

Second, you need to explain which class you want tickets in, and how many together. It's a lot easier in general to get one award ticket per plane than to get more, and the difficulty grows with the number of seats. But agian this could vary from airline to airline, even from destination to destination! And some airlines have better avialability in coach, while others may have better availabliy up front.

Third, availability can vary a lot by destination, and also by date, for the same airline. But the destination that are hard for airline might be easy for another (based on the hub they connect through, etc). Thus without more specifics, it's even harder to generalize.

Finally, things are about to change fast. OpenSkies was just adopted for Europe, and airlines in Europe starting next year will no longer be restricted to hubbing only in their home country. By the time you save up for an award, BA might be offering flights from France or Germany, Lufthansa from England or Spain, KLM from Germany or Ireland. Who knows? (And new routes often have the best availability!)

Meanwhile, Delta is going through a rash of European expansion right now (with its own planes). Again, new routes often have the best availability, but if they're expanding now and you have to save up those miles for a year or two, they won't be new by then.

Lastly, remember the every airline has good availability, as long as you're willing pay double the miles ("standard" awards)! What has limited availability is simply the "saver" awards, which are restricted more or less like restricted deep discount fares are...