Depends on the situation. All the GLs can do a lot more with their rings than just make constructs, and Alan can do even more than them because his power is rooted in magic. He's used it to create and contain singularities, teleport, rejuvenate his body (which makes you wonder why he's still missing an eye), and a whole host of other things. Johns has depowered Alan a lot over the course of JSA, though--he and Goyer brought back the wood weakness before the series started, he aged Alan back up to a 50-something body and made him channel the Starheart through his ring again so he could feel "more human," and he's relegated Alan to just making constructs ever since.
As for the titles you listed with Alan: He was barely in 52, his only notable appearances being when he showed up back on Earth and when he participated in WWIII along with the rest of the JSA. He was great in Checkmate, but Greg Rucka booted him out of the organization and the series after only a handful of issues. He still has some presence in JSA, but as Trop noted, he's been marginalized in favor of the newer members. So he does ostensibly have a big presence in the DC universe, but it always breaks down to just fleeting glimpses here and there. There aren't any comics that are really giving us a chance to dig deep into Alan as a character rather than just seeing him as a figurehead for "the old guard." I'd even settle for just seeing him use his powers in an impressive way at this point. Well, there's JSA Classified, which has had a few Alan-centric stories, but they've mostly sucked.
Personally, I'm looking forward to the upcoming Superman Confidential issue where we see Superman and Alan meet for the first time. That one looks like it'll pay Alan the respect he deserves as the post-Crisis equivalent in the Golden Age to what Superman is in the Silver Age.