I use both of those sites regularly and have never had a problem. I find that AF's prices aren't as cheap as they were and you have to be careful with some things (roasted peppers, olives and the like esp.) because they aren't much cheaper, but a lot of the stuff is fab. I usually use it for things like dried pulses, crisps, snacky things and the like. Got a great buy of 12 tins of crab for £5 a couple of weeks ago and 3 tins of mackerel salad for £1.20 (DS1 and 3 love this), also 5kg of pasta for £1.29
Every now and then you get ridiculous things like boxes of cupcakes for 1p or a case of Angel Delight for £1. My 2 eldest boys use them as well to buy cans of juice and bars of chocolate for their room.
Food Bargains doesn't have as much stuff but can be cheaper and you do get the odd outrageous thing. I fed DS1 and 2's Mountain Dew addiction (roleplaying noobs) last month for a fraction of the price, They had it for 4 cans for £1, so the boys got 2 months supply as well as a month's worth of that American peanut butter and jelly stuff 
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If you buy from AF, your basket keeps a running total of how much you are "saving" and how much your parcel weighs, so you will be able to see for yourself if it's worth the postage.