Are future upgrades possible? It comes down to other parts too. Is the reason you won't be able to overclock because it will be a store-bought, locked-BIOS machine, or because (at least for now) you've been told not to?
I see a lot of "if-thens" to this decision.
I'd rather have a 965BE on a 990X or 990FX board than an i3-3220 on H61 because of the future upgrade potential, overclocking (if possible), and faster interfaces (SATA 6Gb/s and USB3.0). OTOH, I'd prefer the i3-3200 on a Z77 to a 965BE on an 880G or 760G motherboard.
If for whatever reason no upgrades will ever be possible, I think I'd prefer the 965 with the HD7850. If future upgrades ARE a possibility, I'd take the i3 even if it meant having to lower some settings for a while.
Any more information you have about these two systems will be helpful to reach the best choice.
Edit: If this decision is based on this limited "snapshot," I agree with envy14tpe that overall, the 965/HD7850 will provide the better experience. Multi-player games in particular are likely to benefit more from the additional (slower) cores with a more powerful GPU than they would from fewer but faster cores and a mediocre graphics card.