Why is Samaritan smarter than the Machine?

Spoilers for the whole series up to S04E11!

Here is a (maybe non-complete) list of reasons why Samaritan seems to be better than the Machine:

• As @mattiav27 mentions in the comments, the Machine has moral standards, hence the Machine will do not anything immoral to reach a greater goal. While Samaritan will stop at nothing.
• Samaritan has a lot more assets to fight with her. Clearly, Reese, Shaw and root are highly skilled, but it seems that Samaritan has hundreds of assets. Also, don't forget about the challenge in S04E02 where Samaritan recruited very skilled highly intelligent people.
• Team Machine has to hide and can only operate in the dark, while Team Samaritan has assets in the government.
• The Machine is a closed system, while Samaritan is open. The Machine can only communicate very indirectly with Finch & Co. Also, the Machine deletes her memory every night (as it was mentioned in S02E21). Only Root can communicate directly with the Machine (which is difficult in Season 4). In contrast, Greer & Co have full access to Samaritan: they can find certain people, can spy on everyone (and get every record on that -- the Machine would only give a hint if there will be a murder related to that person or not), etc.

Why can Samaritan do things that the Machine can't?

This is due to the design decision Finch made. You can see that in the flashbacks of S04E05, where an old version of the Machine tried to kill Finch. There are two main design principles in Finch's mind when he created the Machine: The Machine must have a high moral compass (e.g. he teaches the Machine in S04E11 that no one - not even him - is more important than anyone else), and access to the Machine should be as restricted as possible, such that no one is able to use the Machine for his own needs, or even to manipulate the Machine. In the flashback of S02E14, you can see how angry Finch is at Ingram when he realizes that there is a backdoor to the Machine - which is the root cause for the numbers, the Ordos storyline, the virus storyline, etc.

Why must Finch, Root, Reese, Shaw and Bear hide?

In the season 3 finale, Greer convinces Control & Co that Samaritan has saved them all, while the Machine even did not see that event coming. Control has seen that Finch is willing to tell the public about the Machine, which makes Finch an enemy of the state: police are searching for them. The bigger problem is that Samaritan is searching for them, which is why they cannot attract attention (which is why the Machine can locate Shaw in S04E08). Finch & Co. are more or less the only antagonists of Samaritan, hence Greer wants them dead.