Technically speaking, there is very little in the way of differences in power between members of the House and of the Senate. Members of each house have one vote on every proposal that is put before them. Thus, they have similar powers. Members of the Senate do get to vote on some things that members of the House do not, such as on appointments to the Supreme Court or to other high governmental positions. Members of the House can originate spending bills while members of the Senate cannot. Otherwise, though, their powers are similar.
When we look a little deeper, though, senators have more power. For one thing, each senator is more important because there are only 100 senators while there are 435 members of the House. Beyond sheer numbers, though, Senate traditions give senators more power. Individual senators can put a “hold” on a judicial nomination. Individual senators can launch filibusters. Individual senators can propose amendments to bills whenever they like whereas members of the House cannot if the Rules Committee does not allow them to.
Thus, though members of the two Houses have similar official powers, Senators have more power due to the rules and traditions of the Senate and its smaller size.