The role of the VP (besides breaking ties in the Senate) is to wake up every day, check the president’s pulse, and execute the president’s agenda. He does not sign legislation, he does not create executive orders, he does not enact any policies. the Vice President does nothing. President of the Senate is a ceremonial role. He can break ties in the Senate, but the filibuster makes those almost non-existent. The President may give him power as an adviser, but it's the same power the President could give a friend, or, in the case of Donald Trump, his own daughter and son-in-law.
The Speaker on the other hand, sets the agenda for the House, brings legislation (or doesn’t) to the floor, and influences the majority on how to vote. It’s pretty safe to say if the speaker doesn’t like a bill it may not ever see the light of day. 6park.com

The Vice President is the second-most powerful official in the Executive Branch, and the Speaker is the most “powerful” person in the House of Representatives while having no official power. The Speaker is elected through the House itself, and the Vice President is elected by the Electoral College, and the results are certified by Congress. The Speaker and Vice President, currently both women, lead the federal government to help Americans around the country.
The VPOTUS:
Election:
Elected by the Electoral College
The Electoral College is a group of people who meet in their respective state Capitols to cast their vote for President. Each state is entitled to as many electors as they are Senators and Congresspeople. Since 1824, the electors have been bound to vote for whom their state’s voters have selected to be the next President. Whoever crosses 270 votes, one more than half of the 538 electoral votes in the country, wins the election.
Certified by Congress
Once the Electoral College votes, the results are passed on to Congress where they are passed by both the Senate and the House. When they have been certified, the President-Elect and Vice President-Elect will be inaugurated on January 20th.
Powers:
Presidential Advisor: The Vice President may advise the President on policy, strategy, or anything. Sometimes, especially if the President is a former governor, the Vice President may advise the President on issues. The Vice President may also bring ideological balance to the White House, and make sure the policies the President enforces work for ALL Americans.Governing Partner: The Vice President may help govern the country along with the President. The VP may come up with a policy that is still signed by the President and passed through Congress (some of the time). Mike Pence was appointed to lead the COVID Task Force, and Joe Biden handled the situation in Iraq when he was Obama’s VP.Congressional Ambassador: Most previous Presidents have been governors, often unfamiliar with Congress. The Vice President may be better at communicating with the Speaker and Senate Majority Leader than the President is for that reason.National Security Council Member: The Vice President attends meetings in the Situation Room of the White House.The representative at events: The Vice President may attend events where the President cannot.
The Vice President is term-limited to 4 years and may run for re-election as many times as they want, as long as they remain eligible for the Presidency.
Speaker of the House:
Election:
The Speaker is elected by all 435 members of the House of Representatives.Most of the time, Democrats vote for the Democratic candidate and Republicans vote for the Republican candidate.Elected at the start of the New Congress
Powers:
Negotiates with the President and Senate: The Speaker is the leader of the House and negotiates with the other people who pass legislation. This is especially true if the Speaker is the opposite party of the President and/or the Senate Majority Leader. For example, if a moderate Democratic Speaker served alongside a conservative Republican President, the President would have an easier time passing his agenda than if the Speaker were more progressive. Contrary to that, if there was a moderate Democratic President as well as a progressive Speaker, the President’s agenda may become more progressive.Leads their party in the House: Usually, most party members vote the way the Speaker does. If a bill has bipartisan cosponsors, the Speaker may decide whether it passes or not. The Speaker’s policy positions may influence how extreme members’ bills will be.Appoints officials in the House: The Historian, Parliamentarian, Inspector General, and General Counsel are appointed by the Speaker.
Comparison
The Speaker is more independent of the Vice PresidentThe Vice President can pass their own policy proposalsThe Speaker controls what goes through the House (most of the time)The VP is a member of the Cabinet and NatSec CouncilThe Speaker can serve for however long they are electedThe Speaker negotiates while the VP advises

Overall, the Speaker of the House is more powerful than the Vice President. The Speaker can stop or pass any legislation that goes through the House, and even stop it from being brought to the floor. The Speaker has more say over policy than the VP does (unless you’re Dick Cheney), and usually serves in office for longer. While the VP has more publicity, the Speaker can control the policies that affect Americans.