Both are reliable - certainly been my experience. For me, the key difference between the two is shipping/speed, parts availability and flexibility at check out.
Shipping: Partsouq typically ship DHL and there shipping quote is reasonable for most small items (Anayama was more expensive for express shipping in my limited experience). Anayama can ship express or surface mail. So I use Anayama and the cheap option of surface mail, when the DHL quote becomes more than the value of parts.
Availability: Partsouq won't wait around for parts to come back into stock - either its available or not (so you might have selected the last gasket in stock - only to find its not available, and the order is amended and sent without!). Anayama do offer a more relaxed pace - you'll get asked whether you want to hang around for a month to see whether parts come back into stock etc.
Flexibility: Parsouq won't allow you to add parts to the order, once submitted. Anayama do give an option of adding parts to the order.