Weezer is – and has always been – a power-pop outfit. Back in 1994, Rivers Cuomo – Weezer’s famously nut so frontman-songwriter – told us in song that Kiss was his favorite rock group. You can’t ignore a declaration of intent like that. The band’s second album, the dark, emo-spawning “Pinkerton” wasn’t the real Weezer, even though it’s the Weezer everyone likes. Indeed, some selective fans hate the more upbeat big-guitar sound of Weezer’s recent work: the “Green” album (2001) and “Maladroit” (2002).

These fans won’t find much to like in “Make Believe,” Weezer’s newest album, out today. It’s a mishmash of styles: hair rock, grunge, New Wave, and pop all bounce together. The album is strongest when Cuomo’s tight songwriting adopts one or two of these sources; it’s weakest on several tracks that bang them all in and wind up not sounding like much at all.

What sets “Make Believe” apart is Cuomo’s once again crystallizing his miserable-outsider persona into an album that – despite its gloss and breezy pop – comes across as conflicted and compelling. On the first single, “Beverly Hills,” he sings: ” I never went to boarding schools / preppy girls never looked at me.” Are we really supposed to take this kind of pain seriously?

I have no idea, and it’s unclear whether Cuomo does either; but the ambiguity, combined with a ferociously catchy hook, make for a great pop song. “We Are All on Drugs,” chugging along on its updated Cheap Trick guitar drive, is almost certainly arch, but I’m betting it will see plenty of play at parties where the title is descriptive. Embracing these sometimes capricious contradictions is what listening to Weezer is all about.

“Make Believe” is by no means a great album – there are too many average tracks, doubly frustrating considering these 12 were reportedly chosen from more than 70 candidates. It peaks late, with “The Other Way” and “Freak Me Out.” In the former the tension is explicit: As the helpless narrator turns away from everything he’s afraid of screwing up, the track sails higher and higher on Pat Wilson’s driving beat, a sunny guitar line, hand-claps, and Buddy Holly back-up harmony. The song is everything pop aspires to be: contradictory, liberating, smart, dumb. The only thing to do is sing along.

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“You have to hear this. It is soooo cute.” Entirely unaware of the presence of any music critics, the bartender at an otherwise deserted Midtown lounge put on “Gracie” from Ben Folds’s new album, “Songs for Silverman,” written for Folds’s daughter. She let the first 20 seconds play, then pauses it to repeat the first line herself: “‘You can’t fool me, I saw you when you came out.’ It’s the sweetest!” Then she restarts the track to let Folds finish his song.

Ben Folds has made a career out of writing observant songs that channel the musical heydays of Billy Joel and Elton John while convincing fans that he’s on to something resonant and special. There’s something shockingly shuttered about Folds’s eagerness to entrench himself in a suburban, middle-class frame of reference, and he knows it.

His first solo release, “Rockin’ the Suburbs,” reveled in its own demo graphic particularity to occasionally tiresome extremes. On “Songs for Silverman,” the same Ben Folds is present, but his maturation is obvious. His observations seem less judgmental, more introspective, without losing any of their clarity or lyrical spark. On songs like “Jesusland” and “Landed,” he examines crises through the lens of elegant pop metaphor with an eye that is wearily observant, but not jaded.

“Songs for Silverman” is also his most musically dynamic album to date. Folds’s piano-based pop has sometimes been swallowed by its own proficiency: it’s fine in a coffee bar, but too smooth to play at home and still respect yourself in the morning. With this album, Folds stated that his goal was to be “spiritually tight, not necessarily musically tight.” The album profits enormously – playing in a piano, bass, and drums arrangement, the sound is “adult” enough to please his fans while perhaps winning converts from some who’ve found his previous efforts cloying in their sheen.

And, for the record, “Gracie” is indeed a remarkably sweet song.

Weezer plays Roseland May 11 and 12 (239 W. 52nd Street, between Broadway and Eighth Avenue, 212-247-0200).

Ben Folds plays Town Hall May 10 (123 W. 43rd Street, between Sixth Avenue & Broadway, 212-997-1003).