I rarely watch YouTube videos, so I don't know what they said but here are some general differences:
1. ODROID-C1 clocks its Cortex-A5 CPUs at 1.5GHz. RasPi 2 clocks its Cortex-A7 cores at 900 MHz. While the A7 is a little faster than the A5, the C1 wins overall.
2. Both SoCs have 512KB level-2 cache shared by the four cores. Each ODROID-C1 core has 32KB level-1 instruction and data caches. I don't know what RasPi 2 has.
3. RasPi has an ordinary SD card, which should go up to Class 10. ODROID-C1 allows Class 10 and UHS-1, which is faster. ODROID-C1 also has an eMMC option, which is even faster. So if your application is limited by mass storage performance, ODROID-C1 wins.
4. RasPi does 10/100 Mb/s Ethernet using its USB hub chip. ODROID-C1 has a dedicated 10/100/1G Ethernet port, so if your application is limited by Ethernet performance, ODROID-C1 wins by a wide margin.
I've been using ODROID-C1 as my primary computer for a couple weeks now and it works very well. There were some initial hiccups, mostly solved or worked around. I'm still having trouble with lost or repeated keystrokes and mouse clicks, but I think I can fix it when the cable I've ordered arrives. These sorts of issues are usually present with a new board -- we saw them with BeagleBoard and Raspberry Pi when they first came out. Part of the learning experience and part of the fun, n'est-ce pas?
Yes, I fully agree. The odroid is fine. The only thing that is worse is the community is rather smaller than the raspi one. But the support seems to be good. So it is nothing for people who like "working-out-of-the-box-solutions". You need some skills with linux and single-board computers to have fun with it. But it has sureley a wider range of possibilities than the new Raspi-board.
Not an impressive video. Boot times are a crude comparison anyway, and when you boot the one to the Ubuntu desktop and the other to the Raspbian desktop you're not even comparing like for like. I've got both boards and use them in headless mode. The C1 does not just benchmark faster, it is clearly faster in real use - noticeably, but not overwhelmingly, so. It is easy to see why.
John summarises it well above. What I might add to his list is:
Faster memory interface, giving much higher memory bandwidth on the C1.
Better I/O architecture. The Amlogic SoC on the C1 exposes two USB buses and another bus for gigabit Ethernet. The RPi's Broadcom SoC gives you just the one USB bus which the RPi uses to drive all 4 USB ports and the 100Mb Ethernet interface. For any I/O heavy application the RPi2 will bottleneck much sooner.
Despite this, there are very good reasons why you might want to go for the RPi2 anyway.
Like all boards (including the original RPi), the C1 has some small-but-annoying teething problems that will have to be ironed out over the next few months. The RPi2 dodges that process because it's mostly identical to the RPi1 and benefits from the platform's maturity.
The RPi community is much larger. While HardKernel does a pretty good job supporting their boards, they can't possibly match the RPi(2) juggernaut - with the one notable exception of Android.
A few years down the line, when the C1 has been abandoned for 64-bit ARM boards, you'll probably still be able to buy a RPi2 and get updates for it.
The C1 has the better hardware. But the RPi2 is still pretty good, more mature, and has a larger community. Both boards are great in their own way. Take your pick.
