Normally, I would have recommended neither of the two combos. If the budget system with integrated graphics were for me, I would have gotten either the E2160 with a better motherboard than any G31-based one (this means a G33 or G35 chipset), or a faster AMD processor than the x2 4000+ (e.g. the x2 5200+ or 5600+) with the AMD/ATi chipset-based motherboard.
But then again, this is a “budget” system whose primary use is word processing, music/video downloads and web-surfing, with some limited gaming (using older titles) thrown in for good measure. In this case, I’d give the nod to the AMD system simply because it’s better balanced in performance. The Intel system has a quite potent “budget” processor – but why drag down its potential with underperformance integrated graphics? In addition, the G31 chipset still uses the old ICH7 southbridge (which dates back to the days of the i945 series chipsets), with its native support for only four SATA devices and no AHCI or RAID support, while the G31 chipset’s MCH supports only four banks (ranks) of memory total (this results in the inclusion of only two DIMM slots on most G31 motherboards, and two double-sided DIMM modules already make up four banks of memory).