AMD AM3+ is basically a 5 year old design. Been about three release of the FX series chips. Early ones were fairly abyssmal, second generation were competitive price wise, third release was mostly power efficiency.
Core count is not a good comparison. On the FX series AMD uses dual core packages that share resources. So effectively 6 core = 3 real cores in terms of cache, ALU, etc.
Instructions per cycle and power efficiency. Intel wins hands down. So that 3.2Ghz Intel chip is faster then the FX running at 4.0Ghz.
AMD cheaper platform, older tech (motherboards lack things like M.2, NVMe, SataExpress, etc), but all are capable of overclocking.
Intel, more expensive, newer technology, faster for gaming, and their mid-range chips compete well with AMDs best chips. Overclocking only on high end chips and boards.