In terms of overall gaming performance, the Intel Celeron E1200 Dual-Core 1.6GHz is very slightly better than the Intel Pentium D 820 2.8GHz when it comes to running the latest games. This also means it will be less likely to bottleneck more powerful GPUs, allowing them to achieve more of their gaming performance potential.
The Celeron E1200 Dual-Core was released over a year more recently than the Pentium D 820, and so the Celeron E1200 Dual-Core is likely to have better levels of support, and will be more optimized for running the latest games.
The Celeron E1200 Dual-Core and the Pentium D 820 both have 2 cores, and so are quite likely to struggle with the latest games, or at least bottleneck high-end graphics cards when running them. With a decent accompanying GPU, the Celeron E1200 Dual-Core and the Pentium D 820 may still be able to run slightly older games fairly effectively.
More important for gaming than the number of cores and threads is the clock rate. Problematically, unless the two CPUs are from the same family, this can only serve as a general guide and nothing like an exact comparison, because the clock cycles per instruction (CPI) will vary so much.
The Celeron E1200 Dual-Core and Pentium D 820 are not from the same family of CPUs, so their clock speeds are by no means directly comparable. Bear in mind, then, that while the Pentium D 820 has a 1.2 GHz faster frequency, this is not always an indicator that it will be superior in performance, despite frequency being crucial when trying to avoid GPU bottlenecking. In this case, however, the difference is probably a good indicator that the is superior.
Aside from the clock rate, the next-most important CPU features for PC game performance are L2 and L3 cache size. Faster than RAM, the more cache available, the more data that can be stored for lightning-fast retrieval. L1 Cache is not usually an issue anymore for gaming, with most high-end CPUs eking out about the same L1 performance, and L2 is more important than L3 - but L3 is still important if you want to reach the highest levels of performance. Bear in mind that although it is better to have a larger cache, the larger it is, the higher the latency, so a balance has to be struck.
The Pentium D 820 has a 1536 KB bigger L2 cache than the Celeron E1200 Dual-Core, but neither of the CPUs have L3 caches, so the Pentium D 820 wins out in this area with its larger L2 cache.
The maximum Thermal Design Power is the power in Watts that the CPU will consume in the worst case scenario. The lithography is the semiconductor manufacturing technology being used to create the CPU - the smaller this is, the more transistors that can be fit into the CPU, and the closer the connections. For both the lithography and the TDP, it is the lower the better, because a lower number means a lower amount of power is necessary to run the CPU, and consequently a lower amount of heat is produced.
The Celeron E1200 Dual-Core has a 30 Watt lower Maximum TDP than the Pentium D 820, and was created with a 25 nm smaller manufacturing technology. What this means is the Celeron E1200 Dual-Core will consume significantly less power and consequently produce less heat, enabling more prolonged computational tasks with fewer adverse effects. This will lower your yearly electricity bill significantly, as well as prevent you from having to invest in extra cooling mechanisms (unless you overclock).