Not in particular, a quick comparison below. A B350 motherboard will let you overclock any Ryzen CPU, and the R3-1200 is a decent processor, similar to a slightly older Intel i5.
I'd be hard pressed to recommend an Intel i5 right now. They are good processors, just not much of an upgrade path. An R3 build will let you upgrade to an R5 or R7, 4C/8T, 6C/12T, 8C/16T all with the same socket.
A brand new Intel i5 gets you a quad core with good IPC, the potential to upgrade to an i7 4C/8T CPU, and not much else. You have to spend extra to get overclocking, on both the CPU, Motherboard, and your own CPU cooler.
Intel does have a new release coming with 6C and 6C/12T CPUs and might be a better choice for gaming in the near future. AMD has the budget quad core market pretty well rounded out.
PCPartPicker part list /
Price breakdown by merchant
CPU: AMD - Ryzen 3 1200 3.1GHz Quad-Core Processor ($108.89 @ OutletPC)
Motherboard: ASRock - AB350M Micro ATX AM4 Motherboard ($59.99 @ Newegg)
Memory: G.Skill - Ripjaws V Series 8GB (2 x 4GB) DDR4-2666 Memory ($73.99 @ Newegg)
Total: $242.87
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2017-08-31 16:32 EDT-0400
PCPartPicker part list /
Price breakdown by merchant
CPU: Intel - Core i5-7400 3.0GHz Quad-Core Processor ($173.99 @ SuperBiiz)
Motherboard: MSI - B250M PRO-VDH Micro ATX LGA1151 Motherboard ($64.99 @ B&H)
Memory: G.Skill - Ripjaws V Series 8GB (2 x 4GB) DDR4-2666 Memory ($73.99 @ Newegg)
Total: $312.97
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2017-08-31 16:33 EDT-0400