This could get a bit complex as there are various things to account for- both the PS3 and 360 are not quite as hackable as the say the wii or the original xbox or the handhelds and MS and Sony have done a bit to counter things as times goes on. I do not consider hacking either that troublesome but it is not as simple as the wii or the original xbox which amounted to simple software hacks and I have been playing around with electronics and computers for years so I am probably not the person to ask here.
Equally the PS3 scene has if not died out then not kept up to date with Sony's counters which is odd from a technical standpoint but hey it is what it is.
Copied games- probably the 360 with a DVD hack. This only allows simple copied games though with a few minor things like savegame hacking and DLC injection of a handful of DLC (stuff like borderlands double pack and fallout expansions that come as installers). Originally it was a matter of flashing the drive (easy enough for most older versions of the drives) and burning games with an image burner but today flashing can be a bit harder (some of the slims especially) and for many new games you will need a hacked DVD burner (nice drives that are common and cost about the same as a normal DVD drive).
http://jungleflasher.../downloads.html has a nice tutorial.
Homebrew- the 360 has some (mainly a handful of playable but crude emulators and some proof of concept stuff) but most of it revolves around copied games and things there and it is nowhere near the original xbox or wii. The PS3 has a bit more for some reason (some more polished emulators and not quite proof of concept but not XBMC grade) but I would still not place it alongside the wii or original xbox. For proper homebrew on the 360 you need a JTAG hacked or Reset Glitch Hacked (RGH) box- both come at the cost of online play (DVD hacks occasionally get banned although nobody has in a couple of years now- we still advise a fatalistic attitude though and to take proper precautions). JTAG requires a box that has not been updated since August 2009 and some minor wiring and basic components where RGH can be done on most (although MS threw a wrench into the works a month or two back) with a fairly cheap chip (about half the price of a game for the top end stuff). Both JTAG and RGH though have region free*, game hacks, menu hacks (things like control remapping), hard drive (USB and onboard), XBLA and DLC loading and more although do note that for the time being (there has been some interesting work of late) you will probably also want to combine it with a DVD hack.
*Europe has some pretty nice western RPGs come out first and can take a while to appear stateside and Japan has a fair few shmups if you like that sort of thing so it is nice to have even if you have a NA console.
Equally Sony blocked much of PS3 homebrew methods so you need to downgrade (I am not so familiar with current PS3 downgrading) or get a console that has not been updated which means you more or less can not play new games (and I guess that means no access to PSN either- there were a few methods for a while but Sony seemed to have studied basic network security since that whole hacking debacle).
Longevity... given how similar the PS3 and 360 are in terms of capabilities and that games companies are spending silly money making them and not to mention the wii U being speculated to only be marginally better than both of those I imagine both will be tossed the odd port for years to come.
I will leave it you to decide if any of the exclusives are dealbreakers for you (the 360 gets most of the RPGs with the exception of disgaea and atelier and maybe just the edge in multiplatform versions but there is little in it- again games companies are in the must spend money phase rather than anything else more sensible and so exclusives are less of a thing than they once were and if you have a PC then 360 exclusives are even fewer and most of those you probably can play otherwise or not miss much with both platforms tending to get the sequels to exclusives be they spiritual or conventional- no demon's souls on the 360 but there was dark souls for instance). I normally dislike linking wikipedia but as this is a simple list comparing session
http://en.wikipedia...._Xbox_360_games and
https://en.wikipedia...Station_3_games