Alright, I'm going to come at this from a political science perspective rather than an average observer spectrum whose going "America Won!". Doing this because I actually would like to discuss politically who won here. Going to try to be objective
The President - Obama comes out a winner here, though not quite as much as he would've if this happened earlier. Ultimately after 2010 Obama needed to pull a Clinton and angle center a bit. He's not done it nearly as well as Clinton did, but cutting the budget was one of the few things he did try to use to make that move. Getting a budget passed, and having it with cuts, is a benefit to him politically.
The Republicans - This is primarily the House Republicans here, and I think they absolutely came out a winner. While some of the social riders did not get passed, the primary thing they were focused on...reducing of the budget...succeeded. From the start of the CR's they've cut $53 billion, which is only about $10 billion less than their original compromised number they through out. Not a bad result. Yes, their riders failed, however I think they were more bargaining chips than anything. Many of the Tea Party House Republicans will benefit far more due to the cut in budget and the fact they stayed firm on THAT issue, as many Tea Partiers main concern was electing people to see them immedietely abandon what they were saying. I think the Republicans would've been far more hurt if they had got to keep some of the social riders and yet didn't cut the budget as much. This budget battle showed, at least in the short term, that these new Republicans aren't going to compromise away their fiscal principles largely.
The Democrats - This is a wash here I believe. They get points for not having the government shut down, which I believe would've hurt them greatly due to their constituents being largely affected. At the same time, you had the Republicans driving home that this should've been passed 6 months ago when they had a majority compared to the Democrats saying Republicans wanted to take away women's health care. I think the more realistic and less sensationalized message is going to be the more lasting one. The debate here was simply not in their favor. While they can sell the removal of the riders to their people, essentially they gave the Republicans what they wanted and in return got to have the Republicans to remove the bonus content on top.
So Obama helped himself some, Republicans helped themselves a decent bit, and the Democrats came out neutral to a bit down.
This entire time though is going to be a mostly afterthought to all but government workers. 2012's budget fight is going to be far more important to all of them, with Republicans pushing for an actual significant cut, Democrats fighting for what they think is more reasonable, and Obama straddled with the situation of figuring where to fall and how to play it. The next 6 months is going to be very interesting budgetarily