According to Oleg Smirnov and Charles Smith, the overall difference does not matter all that much (Emphasis mine)
Our results suggest that membership change in the Supreme Court has a discernable effect on the revealed policy positions of sitting justices. At the aggregate level, the Court seems to move to counter-balance the ideological change brought about by a new justice. One possible implication of the result, which we discuss in greater detail below, is that such counter-balancing behavior may provide greater institutional stability of the Supreme Court. The contrarian movement of drag ensures an institutional rigidity that lessens any new member’s ability to move the aggregated policy position of the Court in any substantial fashion... In other words, membership change in the conservative direction leads to a greater response from liberal justices while a change in the liberal direction leads to a greater response from the conservative justices.And as such when Sandra Day O'Connor, the media continued to portray the already moderate Anthony Kennedy as the new swing vote. Now, we understand that in general that the Supreme Court does try to maintain a certain status quo, and Andrew Gelman too asks why that is so while showing nifty graphs of it. This would then suggest that for a Supreme Court pick to matter, there would have to come a general ideological shift, and historically, it seems that the SCOTUS does reflect somewhat the ideological shifts of the country as a whole.
What does this mean? Well, for Obama, it may seem to be that he had might as well nominate a women, or an Hispanic, or a member of the LGBT community (or all three for special bonus points), to placate his liberal constituencies (especially since his inaction on gay issues have angered the LGBT community somewhat). It's fairly obvious that he will pick a liberal nominee, but if the court is mostly self-correcting when it comes to ideology, how ideologically sound that nominee is really doesn't matter.
With most of the conservative members of the court being fairly young (and Kennedy and Antonin Scalia at the ripe young ages of 72 and 73 respectively), this may also suggest that the country still is not ready for a change back into more overall liberal trend. If the Reagan era of conservatism is over, then we should theoretically see a noticeable change in the Supreme Court, but it's hard to discern just how that will happen except unfortunate circumstances.
Though, there have only been few major eras of notions of government, from bigger national government (inception 1890s) to smaller (1890s-1930s) to bigger (1930s to 1980s) then to smaller again (where we are now). Perhaps the SCOTUS will then change and it'll just take more years than I think.
I guess my main question here is that even if Obama was replacing a conservative justice, could it really have a significant effect on the court itself? Or will it self-correct itself to a more centrist position?