Labour leaders have traditionally been less powerful than conservative leaders as they have less often been in power. Labour leaders are bound by conference decisions and are constrained by the National Executive Committee between conferences and have not always enjoyed a majority on the National executive Committee. They don't control the appointment of their own deputy; who is separately elected and they can't even choose their own shadow cabinet, which is formed, from a Parliamentary committee elected by a vote by the Parliamentary Labour Party.
However Labour leaders often have power over their parties and can ignore conference decisions. When the Labour leader is Prime Minister, they enjoy all considerable constitutional powers associated with it and have as much authority as the Conservative Prime Minister would have. It is more difficult to challenge a Labour leader and there has only been one challenge in the last twenty years and it was unsuccessful. Whereas since 1975 there have been four challenges to a Conservative leader and two of which were successful.
The expense and complexity of Labour's Electoral College makes challenging a leader unappealing, as it is a difficult process to use in electing a new leader. The new system of choosing the Conservative party leader may have the similar effect as MPs have to vote in a number of ballots to eliminate potential candidates in each round until there are only two remaining candidates and then all members have to vote in a final ballot between the two remaining people.
This is a long process and challenges may seem unappealing especially when there aren't many people who would want to be leader of the Conservative party as seen recently when Michael Howard was the only person to emerge. Labour has used constitutional reform in order to come to power and therefore enhance the powers of the Prime Minister. After using constitutional reform, the "New Labour" party is more appealing to the electorate; as support for old socialist views has declined in recent years.
Labour had wanted to appeal to the middle classes and Liberal democrat supporters for more support and as Prime Minister Blair can now enjoy more dominance over his party and is able to choose his own cabinet. Public support gives the Prime Minister a mandate and this is shown recently by Blair with his use of referendums to discover public opinions in order to produce popular policies. With more support the party looks united and the dominance of the leader increases, as they are then the leader of a more united and successful party.
In the election of leaders, we can see the extent to which leaders are given a mandate to rule the party. In the Conservative party, it is less likely that the leader has full support of their party as it is only MPs who vote for the leader until it reaches a final two candidates and it is only then when ordinary members get a say in who they want to be the leader and by this time the person they wanted may have been voted out of the election. Whereas, Labour members have a more democratic election of their leader where all members get a say in who becomes the next leader and therefore giving the leader more right to rule the party.
Michael Howard of the Conservative party just emerged and wasn't elected so his right to rule can be questioned whereas Blair can dominate his party more due to his higher level of party support. A party can affect a leaders power if they aren't united. A leader must have full support of their party in order to have power by a majority in Parliament. We can see a leader's dominance over their party by their majority in parliament votes as they can be seen as very dominant if they can withstand a lot of rebellions like Blair can due to his large majority.
Because rebellions have little effect on Blair due to his, majority, he can dominate his party because MPs know they will have little effect if they do rebel. When the Major government was in power, we could see that major had less dominance over his party as he had more pressure to please his MPs because rebellions would affect him worse than they would Blair. Leaders can dominate their party with the use of party whips, who maintain discipline through threats and bribes. This dissuades MPs from rebellions as they risk losing job perks.
In some cases backbench MPs have a say over leadership as the leader can tend to change policy to prevent rebellions for example when Wilson backed down from Trade Union reform because the chief whip had said he couldn't get it through the parliamentary party. Conferences have some effect on the power of the leadership as the leader's decisions can be affected by the strong expressions of opinion that can influence them e. g. Conservative leader persuaded to introduce Poll tax immediately rather that phase it in gradually.
However theses conferences have also been seen a simply rallies of supporters meeting in a friendly social environment giving free publicity to the leader and the leader still dominates the party as they can ignore the views expressed in the conferences if they disagree with them. Labour leaders have not had control over party organisation as the party's official governing body is not the cabinet or the shadow cabinet or even the Parliamentary Labour Party but it is the National executive Committee which had been dominated by Trade Unions and Left wingers who were hostile to the leadership.
The National Executive Committee has to approve the party manifesto as well as controlling the key appointments like that of the General Secretary. However there have been reforms to increase the leader's power as key institutions now include the Joint Policy Committee, which is chaired by the Prime Minister who can not appoint his own Cabinet Secretary and directs the National Forum which gives him more support so therefore more dominance of his party.