I regard the 3-4-3 as something of a short term fix. I don't see it as a long-term solution simply because the CBs are not good enough to play 3-4-3, either being too slow (Toure) too rash (Lovren) or prone to bad decision-making (Skrtel/Sahko). Balls into the corners hurt the side too much, forcing players out from the centre and disrupting the defensive line. Counter-aatacking sides in particular are dangerous.
However, what is good is that Rodgers has fixed some of the problems that were perceivable from the beginning of the season, namely too much sideways passing and lack of movement up front. By playing Sterling high and Markovic wide, Coutinho has more options and is much more effective as a consequence. I said last year he was the key to our attack and our best games came when he was on the pitch and in good form. The re-jigged system has revolved around getting the most out of Coutinho (and in fact Sterling has been somewhat sacrificed into the thankless role of running in behind the backline and pinning the back four back).
It's been interesting to see how Rodgers has solved the various problems afflicting the side; the soft midfield (flood it and let Lucas tackle everything), the non-functioning attack (pace and creation of lots of chances), the weak defence (put another CB in and cross your fingers). he desrves credit for coming up with a solution while trying to figure out how to resolved the various issues in the team. Last year he dallied with a 3-5-2 before switching to a more orthodox 4-4-2 witha diamond.
A few weeks back I was very upset at his percieved failure to even address the problems in the side, with the team just mindlessly trundling along. I believe it reached its nadir against United, when all the lessons from the previous weeks were tossed aside. I honestly felt his days were numbered after that, though I did not express that concern out loud.
Now though I feel somewhat more confident. The current formation is getting the most out of our best players (including freeing up Gerrard) and even if it is probably only a temporary solution, it will probably be effective enough to see the side through until Sturridge returns and the new players come into the side in january. That will probably include a new keeper; as an aside I have to say the decision to go with Brad Jones is madness in my opinion (unless he is being shop-windowed). Mignolet, for all his faults, is a far superior keeper (imo). If Liverpool have signed a new keeper (as has been suggested by some papers), it's Jones who should be on the way out, with Mignolet going to the bench.