Seawolf
The quality of the answers you get is going to be related to the amount of information you give - you really need to be very specific about what you fly and what you want to gain to get advice appropriate to your situation.
If getting multi-carrier awards is important then Oneworld is great but even their individual programs differ - on Asia Miles there is a 2 carrier award class as long as one is CX which requires fewer miles than the Oneworld multi-carrier rewards. On the other programs you can't combine carriers on the same award except for the Oneworld Award and some AA combinations with European and South American carriers in AAdvantage.
I think that the only multi-carrier award in STAR Alliance (except for domestic connecting space) is a Europe-South America-North America circle trip available on LH and UA through Miles and More.
Within Oneworld there are big differences in the points required for a particular award - again what you want your points for is important to know to be able to give any sort of helpful advice. For example CP have a 1st class award on BA North America- London- Australia for 150000 miles the equivalent award with Asia Miles is 210000 miles and with AAdvantage I think its 280000 miles. ( Although I'd be a bit reluctant to invest my points in CP until their current situation is clarified!)
If your paid travel is mainly economy class then getting elite status and the consequent upgrade certificates and elite-status bonus points make CP and AA more advantageous. If your paid travel is mainly 1st or Business Class then the class of service bonus you get in Finnair Plus is hard to pass up.
As a Lufthansa Senator Cardholder, I'm in the same situation and have made the decision to switch over to Oneworld for a few reasons.
1) Oneworld's Explorer RTW fare is a much better product in terms of versatility (and miles earning opportunity) than the STAR Alliance RTW fare and the cost in Australia is about the same.
2) Having just flown return Australia - US on QANTAS in 1st class (using some very old BA points) the QF (and I presume BA) product I think is superior to United and Lufthansa. Those 1st-class sleepers are great - better than LH and I have yet to see if I ever will the UA First Suite. (Perhaps I'm just being parochial)
3)The Oneworld multi-carrier awards are just great - they are after all the same as the tickets I actually spend money on. They are expensive in terms of points needed but they now allow you to combine all 7 airlines on one award ticket with no limit on the number of stops as long as you keep to the mileage limit you have chosen. when Lan Chile joins in 2000 the possibilities for that award are going to be awesome!
4) On a personal experience level while I had some excellent inflight service on my way to achieving Senator Status 2 years ago I have found that the service provided by Miles and More when I've had a problem has been appalling and so Lufthansa has been relegated to the "Only To Be Flown If There's No Reasonable Alternative" list.