Here's a quick comparison of the two missions. Differences to follow.
- Name: Origins, Spectral Interpretation, Resource Identification, Security, Regolith Explorer
- Lead Institution(s): NASA (USA), University of Arizona
- Principle Investigator (PI): Dante Lauretta (University of Arizona)
- Target: 101955 Bennu
- Launch date: 8 September 2016
- Return date: 24 September 2024 (anticipated)
- Sample mass: 60 grams - 2 kg (anticipated)
- Science objectives:
- Return and analyze a sample of pristine carbonaceous asteroid regolith in an amount sufficient to study the nature, history, and distribution of its constituent minerals and organic material.
- Map the global properties, chemistry, and mineralogy of a primitive carbonaceous asteroid to characterize its geologic and dynamic history and provide context for the returned samples.
- Document the texture, morphology, geochemistry, and spectral properties of the regolith at the sampling site in situ at scales down to millimeters.
- Measure the Yarkovsky effect (a thermal force on the object) on a potentially hazardous asteroid and constrain the asteroid properties that contribute to this effect.
- Characterize the integrated global properties of a primitive carbonaceous asteroid to allow for direct comparison with ground-based telescopic data of the entire asteroid
- Name: はやぶさ (literally, "Peregrine Falcon") (source)
- Lead Institution(s): JAXA (Japan)
- Principle Investigator (PI): Junichiro Kawaguchi (Institute of Space and Astronautical Science)
- Target: 25143 Itokawa
- Launch date: 9 May 2003
- Sampling date: November 2005
- Return date: 13 June 2010 (recovered June 14, 2010)
- Sample mass: < 1 gram
- Science objectives: (my brief summary of the info from this page)
- Determine and map surface morphology, composition, etc. -- in many ways
- Search for possible asteroid satellites and dust rings
- Reveal history of impacts from other asteroid and comet fragments
- Provide accurate shape and mass determinations
- Establish relationship between 25143 Itokawa and meteorite types (composition, type, history, etc.)
Besides the administration of each project (USA vs. Japan), and the spacecraft themselves, the two missions are fairly similar. There are some notable differences, however, and for the sake of the OP, I'll focus on these.
Due to some failures, most of the spacecraft burned up upon re-entry. The Hayabusa mission returned less than a gram of material. According to Dante Lauretta (PI of OSIRIS-REx) in this publication, the OSIRIS-REx mission is in part an attempt to continue the work of Hayabusa, as OSIRIS-REx was hugely influenced by Hayabusa.
In the same publication, Lauretta points out that Hayabusa's difficulties were due mainly to limited knowledge of Itokawa and insufficient simulation of the sampling process ahead of time. OSIRIS-REx will spend almost a year characterizing Bennu while orbiting it, however, so scientists on Earth will have a better understanding of the asteroid and (importantly) its surface before actually sampling it. Whereas Hayabusa actually landed on Itokawa for about 30 minutes, OSIRIS-REx will touch it only briefly.
Although both Bennu and Itokawa are of similar size (~400-500 m in diameter), a key difference is that Bennu is a near Earth asteroid, meaning that it could collide with Earth, and Itokawa is not. Also, the shape of Itokawa is more like a slightly bent potato, whereas Bennu is much more rounded.
As for technology, Hayabusa used an explosive harpoon to kick up particles into its collection module. OSIRIS-REx will essentially cover the sample site with an inverted pan-like contraption and release several bursts of nitrogen gas at the regolith to kick up particles into its collection module.
Since OSIRIS-REx will spend a year orbiting Bennu, it is equipped with a suite of telescopes/imagers, radar, spectroscopes and gravitometers to keep it busy during this time. Many of these instruments allow collaborative, independent analyses of the inferences made by the other instruments on board. While Hayabusa also had several similar instruments, it did not have as many as OSIRIS-REx.
You can read about the individual instruments on the official pages for Hayabusa (also here) and OSIRIS-REx (also here). These pages, and links therein, can provide you with a wealth of instrumentation and engineering details.
Except where noted, information was taken from Wikipedia's pages on Hayabusa and OSIRIS-REx. Some information was also based on discussions with colleagues involved with OSIRIS-REx.