They both are/were, in their own ways.
First, of all, let's note that both courts' justices scoured the cert petitions to find the cases that presented the issues they wanted to decide. That selection, in itself, is a form of activism, that probably is simply unavoidable.
The courts of the 70s were activist in a somewhat more "substantive" measure - meaning that their method of interpreting the constitution and laws did in fact differ from the way that had been conducted previously. Indeed, if you read some of the old classics, it's actually sort of striking how much they read almost like legislative edicts than traditional legal analysis.
Today's Court is, imo, more activist in a more procedural way. To my eye, they are more aggressive at looking for the cases they want. (And, if there is a problem with organizations like FedSoc, Pacific Legal, and the like, it is that they've created a feedback loop of advocates to create those cases, just as ACLU and NAACP did before them on the left.) Clearly, their use of the shadow docket this last year or two has been inconsistent with prior practice, and while I recognize they have to address the cases that are presented to them, there is absolutely a case to be made that they've been selective in its use. Second, as I remarked regarding Dobbs, in the cases that interest them, they have in fact decided them on bases that are broader than necessary. But as to substantive activism, I would say two things: (i) their approach to decsionmaking is actually consistent with the traditional means that courts used to address cases; and (ii) their decisionmaking is a lot less monolithic than many on the left would suggest. The Gorsuch/Alito split on criminal procedure matters, and the Thomas v. Kav and Barrett perspectives on the real world operation of institutional government, illustrate this nicely.