Epiphone makes top-quality guitars. The only way is to play them both and see what YOU prefer.
But I'd say the Ibanez is inferior- very budget-oriented. Here's a list of people who have used Epiphone over the years:
The Beatles made prominent use of Casinos. In December 1964 Paul McCartney purchased a 1964 Texan FT-79 acoustic and a 1962 Casino; early in 1966 George Harrison and John Lennon followed suit, acquiring Casino E230TDs which they used regularly on stage and in the studio thereafter.[1][2] Lennon's Casino, first used on the album Revolver, became his main studio and stage guitar both with The Beatles and as a solo artist.[1][2] Epiphone produces two John Lennon signature model Casinos: One is a sunburst model resembling Lennon's prior to his alteration of the finish; the second, known as the "Revolution" Casino, is a replica of Lennon's after he had his sunburst Casino professionally sanded down to its natural finish.[3][4] McCartney used his Texan acoustic extensively for songwriting; he also performed the song "Yesterday" on it during an appearance on The Ed Sullivan Show, and still uses this guitar to perform "Yesterday" in current concerts.[1] Epiphone has issued a McCartney signature Texan replicating this guitar.[5]
Keith Richards (The Rolling Stones) was among the first "British Invasion" guitarists to acquire a Casino, using a sunburst model with P-90 pickups and a vibrato tailpiece (most likely a 1961 or 1962 model) on The Rolling Stones' first US tour in June 1964.[6] Although he also used a number of other makes in the mid-60s, photos and footage show Richards continued to use the Casino regularly both on stage and in the studio through 1966.[7]
Brian Jones (The Rolling Stones) used a Casino, notably on "Little Red Rooster" on the band's May 2 1965 appearance on The Ed Sullivan Show.[8]
Dave Davies (Kinks) can be seen playing an Epiphone Casino in the video for "All Day and All of the Night".
Dwight Yoakam uses a Casino Elitist
The Edge (U2) uses a Casino.
Matthew Followill (Kings of Leon) uses a Sheraton II.
Mark Wilson (Jet) used a Jack Cassady Bass in the early videos such as Are you gonna be my girl
Nick Valensi (The Strokes) plays a Riviera which he customized himself with Gibson P-94 pickups; a Nick Valensi Signature model based on it was issued in 2005.
Noel Gallagher has two Epiphone Signature models, issued during the height of Oasis' popularity in 1995-96: the "Noel Gallagher Union Jack" and "Supernova" semi-hollow guitars.
John Lee Hooker used a Sheraton (with Frequensator tailpiece) and Sheraton II (with stopbar bridge). Epiphone introduced a signature John Lee Hooker model in 2000, the year before his death.
Brian Aubert (Silversun Pickups) uses a vintage sunburst Sheraton II as his primary guitar. It can be seen in several videos from the "Carnavas" album.
Tom DeLonge (Blink-182, Angels & Airwaves) uses his signture ES-333 in both Epiphone and Gibson versions.
Ezra Koenig (Vampire Weekend) plays a natural finish Sheraton II.
Matthew Followill (Kings of Leon) plays a vintage sunburst Sheraton II. He has also been pictured with an ebony finsh Sheraton II.
Josh Homme (Queens of the Stone Age) used an ebony Dot around the Lullabies to Paralyze era of the band.
Joe Pass uses an Emperor. Epiphone produces a signature model of Pass' guitar.
Les Paul used Epiphone guitars for recording from the early 1940's until the late 1950's, even after his signature Gibsons were produced. The Epiphones were highly customized models with his own pickups on them.
Ace Frehley (Kiss) uses a customized Les Paul with Dimarzio humbuckers.
Jay Jay French (Twisted Sister) uses a Les Paul. Epiphone produces a Jay Jay French signature model.
Pete Doherty (The Libertines/Babyshambles) uses a Coronet as his main electric guitar.
Steve Marriott (The Small Faces/Humble Pie) used a Dwight during Humble Pie's early days; it can be heard on the track "I Don't Need No Doctor".[9]
Django Reinhardt acquired a Zephyr to play during his American tour with Duke Ellington in 1946. He used the guitar for the rest of his career.[10]
Wayne Static uses a Flying V Signature guitar.
Phil Upchurch is pictured with an Epiphone Casino on the covers of his albums Feeling Blue and Upchurch.
Alex Lifeson (Rush) uses a Masterbuilt acoustic and has appeared in several Epiphone advertisements.
Ernest Tubb used several different acoustic models.
Nancy Wilson uses an Epiphone Les Paul Ultra and has an endorsement from Epiphone.
Frank Iero uses an Epiphone Les Paul Elitist
Then again, I'm a Les Paul player, so I'm biased. But I never played an Ibanez that I cared for.