Depends on what your goal is and what your budget allows. For a work/office PC. A computer powered by an AMD APU makes a lot of sense, they are affordable, and have more than enough grunt for typical office tasks. Likewise for a home theater/media server, an AMD APU is great, they have enough power for the job, and their integrated GPUs are powerful enough to output HD video on the fly.
If you're building a gaming machine, then you want to go with Intel. AMD has basically abandoned the high end of the market, and their fastest CPU, The FX-9590 is bested by Intel's mid-range i5's in most areas and completely outclassed Intel's LGA 1155/1150 i7's in all areas save for price. I won't even go into detail as to how poorly AMD's top offerings compare to Intel's LGA 2011-based CPUs.
With that said there are situations an AMD CPU would be preferable. For example if you were on budget and had somewhat more modest needs then it would be a viable option. For example, I built a computer for a client earlier this year. She didn't need a full-on gaming computer, but she did want it to be able to play some games (BF3, Borderlands, WoW, etc.) But she needed everything (the tower itself, wireless keyboard/mouse, 24 inch monitor,etc.) and wanted to keep it under $1000 for everything.
I thought about doing one of the new (at the time) Kavari APUs, but I found out that I could get better performance for about the same price if I went with an FX-6300 and a low-mid range discrete card. So I went with the FX-6300, with a slight OC and a Radeon R7 260X video card, 8GB RAM, Asus AMD 970 mobo and a 1TB HDD, Corsair Carbide 330R case, Cosair CX600 PSU, and 212+ Hyper (it was on sale, the evo wasn't) cooler. Got a Dell 24 inch IPS panel monitor on sale. And was able to bring it together for $938 for everything. The computer does everything she needs and wants it do. I would've liked to have added a SSD, but the budget wouldn't allow it.
In this case, I had I go with a Haswell i3 or i5, I would've gone over the budget. And in this case the AMD CPU was provided enough performance at the right price. Had it been me, I would've spent the extra money for an i5, but that's not an option for all people.