While the common consensus around here is that you should pick the FFP of the airline you end up flying the most as your primary program, you don't have to follow this. You can very well fly airline A a lot but credit all those flights to a partner airline program if that works out better for your specific needs.

Look at the Finnair plus earning tables for Qatar flights. Right now, Y,B,H,K and M booking classes earn 100% (status qualifying) points in Finnair Plus, L,V,S,N,T and Q earn 50%, and only the three lowest booking classes O, W and G earn just 25%.
With QRPC, only full-fare Y and high-priced B and H fares earn 100%, the number of mid-priced fare classes that earn 75% and 50% is lower and the number of 25%-earning fares higher - including the widely available, discount "T" fares.
So, on average, if flying Qatar in economy on tickets that the average business traveler books (excluding special promo pricing or fare sales) you get more Finnair Plus points flying Qatar than you would get Privilege Plus miles.
Example:
Flying BKK-DOH-FRA and return on QR on a T fare, you'll earn 3,060 qmiles (award miles) and 40 Qpoints (status qualifying points). To qualify for mid-tier QR Gold/oneworld sapphire status, you'll need 300 Qpoints in 12 months. You will have qualified for Gold status only on the return leg of your eight annual trip to Europe.
Flying BKK-DOH-FRA and return on a QR T fare but crediting to Finnair Plus, you will earn 19,700 (status-qualifying) points. With the AY+ Gold status threshold set at 80,000 points, that means you'll have qualified for Finnair Plus Gold/oneworld sapphire status on the outbound leg of your fifth annual flight - twice as quick than if you credited the same flights to Qatars' program.

I only suggested to go with Airberlin topbonus because they will offer a status match from TK (to my knowledge, no other oneworld airline will do this at the moment). The program as such isn't very attractive for you. But you can use your matched status for the benefits while building status on another oneworld airline.

There's a simple logic behind why Qatar flights are cheaper than Finnair's: You will have to connect in Doha going to Europe, and Finnair flies non-stop (Well, to Helsinki...). The operational and economic advantages of having a hub halfway between Europe and Asia in a region with no/low taxation, cheap labor etc. enable lower prices and are the reason why Qatar, Emirates and Etihad have lured so many passengers onto their planes and away from the European and Asian airlines.
Personally, in economy, I don't mind the stop in the middle of the night as sleep is compromised anyway, and the option of having a shower, getting some food and stretching the legs is appreciated. In business class, different story. I can get a night of uninterrupted sleep on a nonstop Europe-Asia flight, which for business travel is crucial as it allows me to hit the ground running.