Republicans did not repeal the filibuster. Since they couldn't avoid a shutdown without either Democratic support or repealing the filibuster, that's a win for those who would like to retain the filibuster to use in the future (when Republicans are next in the Senate minority).
Republicans did "win" the shutdown without giving Democrats anything they weren't already planning on giving them. So they came out of it with about as good a record as people could have expected going into it.
Republicans disconnected the continuing resolution from DACA (Deferred Action for Childhood Arrivals) for the moment. It's unclear what will happen when a DACA bill is brought to the Senate. They have the votes to pass one in the Senate. It's uncertain how many they lose due to whatever other immigration changes get included.
It's uncertain if Donald Trump will support it, although they may have the Senate votes to override a veto (67, and we know they have at least 60 if they can vote for cloture). It's uncertain if it can pass the House much less with veto override supermajority (two thirds of the votes cast, which can be up to 290 if all 435 Representatives vote).
Republicans also have five Democratic Senators in states that voted for Trump on record as supporting shutting down the government in order to avoid immigration reforms. This is relevant, because some of these same Senators may be on record as opposing the concept of shutting down the government over policy.
The next time Republicans vote for a shutdown, many Democrats will be limited in the criticism that they can make. Because the Republicans can now point to the Democrats as having supported a shutdown for policy unrelated to the budget.
The shutdown had minimal actual effect. It closed before a weekend and opened afterward. So other than a few closed parks and some closed federal offices on a Monday, there wasn't much impact.
Beyond all that, Republicans are kind of stuck. On the one side, there is pressure to do something DACA-related that will cover the Dreamers. On the other side, their base wants immigration changes that restrict immigration. While most Americans support DACA reforms, polling something like 75-20 in favor, there's still the 20. That's a small group, but it's one that is mostly Republican. This may not be a winnable situation for Republicans. They may lose either way. Perhaps the best that they can do is to minimize their losses.
How much do Republicans need to get in return for DACA to satisfy their base? We don't know yet. The longer they can delay, the more pressure there is to do something, as DACA expires in March. However, the Democrats feel that pressure more strongly than Republicans. While DACA is popular, even among Republicans, it is more popular among Democrats.
If Republicans offer up a bill that includes DACA and some number of immigration reforms, then it is unclear where that leaves Democrats. Republicans will have kept their promise. Will Democrats be forced to vote for a bill that they don't like? If the form of the bill is publicly popular, this could mean that the next time, people will blame the Democrats for the shutdown. They blinked this time, when polling suggested that Republicans were being hurt more. What would happen if the Democrats were the ones being hurt more?
And all that assumes that the polls showing the Republicans being hurt more were correct. It's possible that the Democrats had polling (or other information) showing that they were actually being hurt worse, possibly in the twelve states with competitive Senate elections. Remember that the national vote is essentially irrelevant in a midterm election. It's the state and district votes that will control the results.