I would go with the Xbox 360 Slim RGH2. I have a Falcon JTAG and a Slim CFW PS3 and it seems some PS3 slims have cooling issues that require removing the heatspreader and applying thermal paste.
I got a CFW PS3 Slim off of eBay and it is loud, I replaced the thermal paste but it still is loud and even shut down on me once from thermal overload. The Xbox 360 Slims on the other hand run near silent and can have the fan speed boosted a bit while still being silent. A lot of this has to do that the PS3 Slim's dual chips (45nm cell, 40nm RSX) vs the Xbox 360 Slim's single 45nm chip.
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When it comes to homebrew, the PS3 wins on that front, whereas the Xbox 360 has very little homebrew games and emulators.
When it comes to hard drive replacement, the 360 wins on this also, you do not need to reinstall all your games or copy them off the original hdd since the original HDD can be connected via usb to the 360 to copy the data over. The PS3 would require copying all the data off the internal HDD to USB then copying it all back to the new drive once installed and formatted.
When it comes to Networking, the PS3 wins on the LAN front with a Gigabit Ethernet controller, which is nice for FTP. Wireless is where it gets iffy, it has a 2.4GHz Wireless G chipset which is quite limited and will slow other wireless N 2.4GHz devices down to G speeds unless your access point supports wireless airtime fairness, which itself has issues with some devices.
The Xbox 360 only has 10/100 connection, but the Xbox 360 Slim's have a 2.4GHz Wireless N chipset so it will not slow down the rest of the wireless devices on 2.4GHz to wireless G speeds when used like the PS3 will.
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When it comes to loading backups, I think the Xbox 360 wins on simplicity and functionality and you can still earn achievements on your Xbox Live account offline via putting your account on a flash drive and signing in while playing a game and signing out before quitting a game, which is safe to do AS LONG as you do not load any homebrew while signed in. afterward, you can use the flash drive on a stock Xbox 360 to sign-in to live and sync the achievements.
NOTE: you will want to use Aurora Dash as your custom Xbox 360 dashboard then download and install Dashlaunch, Dashlaunch is important for a modded 360 since it can unlock XBLA, DLC, and GOD content automatically and can block signing into Xbox Live to avoid banning a Xbox Live account or the console if it is not already banned.
NOTE2: Dashlaunch can adjust SMC fan values so you can have the fans change RPM to hold a set temp or use a fixed fan speed percentage.
The Xbox 360 has several ways of loading backups and unlocked XBLA games (Dashlaunch automatically unlocks most, XM360 homebrew can take care of the leftovers if they are not unlocked)
You can install your own Xbox or Xbox 360 games to the HDD or USB drive via Aurora Dashboard or in NXE format via the 360 normal dashboard [360 games only]. (use NXE2GOD to remove the need to insert disc)
You can copy Games on Demand or XBLA games from another JTAG/RGH console or a stock console then play them on the RGH console as long as Dashlaunch is installed.
You can use FTP to copy stuff to and from the Xbox 360 HDD, connected USB Drives, DVD Drive (read only), and NAND as as Aurora Dash and Dashlaunch both have FTP Server options.
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Where you can install and/or run games:
USB Drive (Extracted and GOD [Games on Demand] format) via FAT32 formatted HDD or Flash Drive
Internal HDD (Extracted and GOD format). Any HDD can be used, although Partition2 (Xbox Emulator) will need to be manually added if using a non Microsoft HDD that does not have it.
DVD Drive (Burned discs work as long as the DVD drive is flashed)
SMB/Windows Share (Never personally tried this)
The Xbox 360 can also load extracted original Xbox games off of the internal HDD as long as Partition2 is there and the hacked 2007 Xbox Emulator files are copied to it.
Original Xbox DLC can be downloaded from various sites online and extracted to the 360 HDD via FTP and will work just fine. This is the only way to get those DLCs as the original Xbox Live service shut down years ago.
The Xbox 360 cannot run any streaming apps other than Windows Media Center and stuff shared via DNLA. All the apps require Xbox Live sign-in to work and there is no way so far to bypass that.
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Now on to the PS3.
The PS3 can load PSP (not very useful, most games do not run right), PS1 and PS2 games (via software emulation, unless on an older FAT PS3) via ISOs (PS2 games) and bin/cue (PS1 games [ISOs are NOT proper PS1 dumps])
PS3 games can run extracted or in ISO format
PS1 games are fully emulated but that was intentional by Sony since day1 so the PS1 emulator works really well and very few games have issues with it. Even problem games like Spyro 3 with it's state of the art copy protection system play fine and you can can use PSN PS1 releases over bin/cue disc rips if you want.
PS2 games are fully emulated so some games have graphical issues, slowdowns, and some crash or not run at all, however this is by no means a deterrent. I have found plenty of good PS2 games that work well enough to play fully.
The PS3 does not have an automatic way to activate some games and PS3 apps so a homebrew app called reactPSN is needed to create a dummy account that is used to tie .rap files (activation licenses) to so the games/apps work.
for ease of use, I recommend to use Rebug CFW on the PS3 (you can install it directly from 3.55 OFW or another CFW) as it has a lot of features and Webman built-in
Webman is an extention/addon to the stock XMB that allows selecting PS1, PS2, PS3, and PSP games to mount right from the games tab then the selected game is mounted as a disc that shows up like if you put a disc in the console yourself.
Webman can control the fan speed if the PS3, which is nice but there is not much room to adjust as the fan is a blower fan so it gets quite a bit louder when ramped up so using higher speeds is quite limited by the loud noise unless you ignore it.
There is no way to safely get Trophies on PS3 games then have them tied to your real PSN account since there is no way to use PSN accounts offline on a USB drive like the 360 can.
The only way would be to turn on features to help hide the CFW from Sony so you can use PSN on CFW but that does not work very well and people have been banned for doing so.
For streaming apps, you can google "PS3 nopsn apps" to find a bunch of streaming apps that have been modified to work without PSN sign-in thus allowing those apps to work on a CFW console unlike Xbox 360.
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Rebug CFW allows installing PKG files, so any games or apps in PKG format can be installed to the console.
Webman has an FTP Server built-in so that can be used to copy stuff to and from the HDD and connected USB drives.
