Of course I realise that this will vary depending on which emperor specifically (I was thinking Maximilian III and Charles V more specifically though) but, generally speaking, how powerful was the emperor? In terms of both military might, and political influence amongst the states of the empire.
I can't speak of Maximilian III, but Charles V's reign as HRE emperor was beset by many challenges. To name several important ones:
Lack of a support system to rule such a large empire. As a result, he was very much a traveling king, both to satisfy the need from various fiefdoms that their ruler should reside with them, and to put pressure on local courts to solve emergent problems. Add to this that different fiefdoms had different rules of government and most importantly how to raise taxes.
Growing imbalance among his possessions, and dependence on bankers to provide finances, backed by reliable income from several of his fiefdoms (Castille, Naples). Whereas other domains provided challenges and little revenue in return. This table provides a great illustration.
Collaboration that turned into sibling rivalry between him and his brother Ferdinand. Although Ferdinand was raised in Spain, he was sent off to Austria and Germany almost as soon as Charles himself arrived in Spain, to stave off the possibility that he may be used as a figurehead by the opposition. As Ferdinand became his regent in the HRE, he pressured Charles to abdicate the HRE emperorship to him, instead of to Charles' son Phillip.
External threats forced internal concessions, namely the French and the Ottomans. Articles in the Peace of Augsburg, an uneasy truce between Catholics and Lutherans, strongly reflect this.
Internal threats forced reforms that led to future conflicts, for example the succession law in the Low Countries was radically altered to ensure the integrity of that territory. While this succeeded in that all of them went to his son Philip, this started a unifying tendency that led indirectly to the Dutch revolt.
Militarily he was very powerful, and won key battles such as Pavia against the French, Muhlberg against the Protestants, Mohacs against the Hungarians, and the relief of Vienna against the Ottomans. But naval security in the Mediterranean eluded him, and it took several decades to be able to beat back Ottoman expansion there.
I skipped over the challenges of Charles' rule in Spain as it is perhaps beyond the scope of this question.