There are many ways of staging an Andy Warhol exhibition, but one of them is probably not the way the Mac in Belfast has done it. Warhol's work is shot through with a kind of blank nihilism. This is not a failing; the cool emptiness underneath its slick surface is part of what makes it interesting and challenging, but the Mac's show comes across as being not so much nihilistic as almost cynical, a bid to convince visitors that they are at a Warhol exhibition when there isn't really much of one there.

It’s only partly the Mac’s fault. Warhol’s material artistic legacy has been regulated and commodified to a daunting degree. Given the factory-like production methods in Warhol’s studio, which he helpfully dubbed the Factory, some retrospective regulation was clearly necessary, since there is a lot of stuff out there with some, often tenuous, connection to him. Authentication or its denial can make or lose fortunes, and there have been bitter disputes, not least because part of the point of Warhol is his undermining of the idea of an authentic, authored artwork.

The bottom line is that it's extremely difficult and expensive to mount a substantial Warhol exhibition. What the Mac had going for it is a considerable amount of goodwill on the part of Tate and the National Gallery of Scotland, the source of a great deal of what's on view. Specifically, most of the show is taken from Artist Rooms, the ambitious touring scheme devised to make use of the jointly acquired Anthony d'Offay donation. This extensive collection of about 750 works overall was purchased from the gallerist, dealer and collector in 2008 for roughly one fifth of its market value.

The most substantial piece in the Belfast show is probably a 1986 four-panel painting, one of Warhol's Camouflage series, which reproduce camouflage patterns. However, Camouflage doesn't disguise the relatively thinness and sketchiness of a great deal of what else there is to see, including cow wallpaper and cloud balloons. A large chunk comprises posters, often for Warhol's films, several of which are being screened, courtesy of the Andy Warhol Museum, Pittsburgh. To describe Warhol as a "vibrant personality", as the gallery does, is surely to misrepresent him, and to say that his very dark, often interminable films "captured the energy of the swinging 1960s" is laughably wide of the mark.

Yet one can see why the Mac wanted to do a Warhol show. The venue has aimed for popularity and accessibility and, like Picasso and Matisse, Warhol is one of the select few bankable names in the pantheon of modern art, one virtually guaranteed to draw a mass audience well beyond habitual gallery-goers. At the entrance to the exhibition, you'll find a raft of merchandise capped by a "Souvenirs" sign.

Lichtenstein's comic language

It's instructive to note that Roy Lichtenstein, a contemporary of Warhol's and also a Pop Art luminary, does not have quite the same cachet with the wider public. He is the subject of a major retrospective already seen in the US

, currently showing at Tate Modern and travelling on to the Pompidou in Paris later in the year. Lichtenstein’s stroke of genius was to translate the language of comics into fine art, recreating frames from comic strips on a massive scale while respecting their graphic, emotional and technological values.

He went on to apply the aesthetics of comics to high-art genres and history and, at some point, he lost a significant proportion of an audience that readily identified with his iconic comic-book imagery but wasn’t quite prepared to go one step further.

He himself did go on, exploring what happens when comic-book techniques meet the traditional pictorial genres of landscape, the nude and abstraction, directly referencing Mondrian and Matisse, for example. He was an exacting, skilled technician and his work is beautifully made. Almost everything included in the retrospective is visually fascinating and witty and, more surprisingly given his Pop Art credentials, on occasion quite austere and minimalist in feeling.

An austere approach

Austere is certainly a word that applies to Sean Scully's Doric at the Hugh Lane Gallery in Dublin. The core of the exhibition is a series of large-scale paintings made since 2008, partly in response to the financial crisis, especially in relation to Greece. In fact, Scully has described the work as an "homage to Greece".

Referring to the “simplicity and force” of the Doric architectural order of classical Greece, he evokes the underlying values of classical civilization.

Appropriately, the paintings were first exhibited in the Pireos annex of the Benaki Museum in Athens last year. The Hugh Lane has built a larger exhibition around them, a really fine, extensive show, in fact, extending back to Scully's earlier works and drawing on the gallery's own significant holdings. The Doric paintings are monumental, like walls composed of massive blocks of stone, grey on grey. They are big, physical presences.

There’s a severity and gravity to them that is uncompromising yet, as usual with Scully, they are much more negotiable, more human and vulnerable than they first appear. On closer inspection, they are layered with nuances.

If the Mac's Warhol is a bid to package culture as entertainment, both Lichtenstein and Doric are something else. They both set out to present us with as much as possible in the way of thoughtfully selected and displayed work, and encourage us to make up our own minds. Each work by Scully is like an argument. It's a proposition that engages you. It may not win you over, you might remain unconvinced, but it's well worth having the argument with it. And the same holds true of Lichtenstein.

Andy Warhol is at the the Mac, 10 Exchange Street, Belfast until April 28th . Doric: Works by Sean Scully is at Dublin City Gallery, The Hugh Lane until June 9th. Lichtenstein: A Retrospective is at Tate Modern, London until May 27th