Stability of organophosphorous vs organophosphates?
Setting the scene for your question

In Environmental Chemistry there are several pathways a chemical might travel through including:


being subjected to the biochemistry of an animal
photodegradation
chemical degradation (perhaps it slowly reacts with water, etc.)
uptake as a metabolite in plants
degradation by soil microorganisms  


and this is ignoring aquatic and air pathways.

Say, within a mouse or a fly, a possible pathway for degradation for some insecticide is cleavage of the P-O bond. How they have determined this in the past is noteworthy; a synthetic chemist would isotope label an atom in the molecule, say $^{33}$P-labeled or $^{14}$C-labeled, and he purified it before finally determining its specific activity. Then a biochemist would dose a mouse with a solution of the compound dissolved in an appropriate solvent, such as olive oil. Urine and feces were collected after administration. An aliquot of the collected urine, for example, would have its radioactivity measured using scintillation counting. The organo-soluble species would be extracted from the rest of the urine and the distribution of radioactivity could then be determined between the aqueous and organic layers. Then one could investigate what were present by TLC if you're old school -- they would actually run, via cochromatography, all the possible metabolite products they could independently think of and synthesize to identify a TLC spot! (That is a lot of work.) These days we can cheat with HPLC-MS. So, you might ask, "are results from this generalizable?" I have to tell you that they generalize in a very rough way. Enzymes are responsible for all the nifty biochemistry and they tend to be rather selective towards a given substrate and, in many cases, chirality even matters! What they are picky about is a tough problem that is tailored to each individual enzyme. One can make all kinds of generalizations about the chemical nature of the bonds and some possible predictions from it, but those won't necessarily hold up in an animal model with a different molecule.

So nitty-gritty mechanisms might not be what we want to look at. Instead we'll step back and take a broader view of this landscape. We need to look at bigger items in terms of physical properties, namely:

1) Persistence: what is its half-life in soil, etc. This is a matter of degradation, whereas the next is all about movement of an intact molecule. A simple chemical way to test this is how they resist hydrolysis.

2) Mobility: over time, does the compound tend to sit or spread itself around?
For example, factors that influence this are:


sorption: how much does our chemical bind to our soil?
water solubility: how easy it is to move in water for our chemical?
vaporizability: how likely is the material to evaporate away from its source?


A famous organophosphate is malathion. The partition coefficient, according to the wiki page, is 2.36. This implies its solubility is greater in organics than water, but some of it will most certainly dissolve in water. I think, based on its size, it is reasonable to assume it has a negligible vapor pressure too. These factors suggest it will have a low mobility: it will tend to stick to organics, won't appreciably evaporate away and will take quite a lot of water to wash it away. Contrast this with a famous organochlorine, DDT, which has an even higher partition coefficient (on the order of 10, so even more sticky and less soluble in water) and an even higher mass (so probably a lower vapor pressure) and thus an even lower mobility. Indeed, organophosphates largely replaced organochlorines as pesticides, in part, because they persist for shorter periods of times in the environment.

Many of these organophosphates were tested by us and their history is relevant. World Wars I and II ushered in a new era of chemical warfare agents and pesticides, notably of the classes of organochlorines, organophosphates and carbamates. Some organophosphates hardly persist at all, such as tetraethyl pyrophosphate, but they are pretty toxic to mammals. Many other organophosphates were screened for low toxicity towards mammals and increased persistence. We actually sought longer-lasting half-lives for these compounds! It turns out that we see alkyl phosphates with shorter lives than the longer-lived aryl species.

We tend to see certain trends within the different organophosphates, such as the water solubility being greater for the less complex and more polar compounds. An ethyl- is less soluble than a methyl- derivative and an aryl-substituted species get partition coefficients approaching those of the organochlorines.

"All this is fine and interesting, but it doesn't have much to do with my direct question," you might say. And most of the above just sets the scene for my answer to your question. Your specific query, I believe, requires us to go back to a nitty-gritty detail which is really only relevant in the case of your comparison between a phosphate (P-O-C) and an organophosphorus compound (P-C).

My answer to your question

In the biochemistry of most life, phosphates are pretty ubiquitous. As a result, many enzymes have evolved to manipulate them in many different forms; one class of these enzymes is called phosphatases and they assist dephosphorylation reactions. They certainly cannot manipulate just any ol' phosphate (hence why more complex phosphates have longer residues). We could say organophosphates are more "natural" than your typical organophosphorus compound. There is, therefore, a greater chance of having a tool -- an enzyme -- that can pick your more "natural" looking compound apart than your harder to find P-C bond.

As you've indicated, these phosphates are actually pretty stable. It's why DNA is built using them! But when you compare the bond lengths between P-C and P-O and O-C, there's a decent chance of finding that a P-C bond length is longer than a P-O or O-C. This leads me to believe that there are many cases in which P-O and O-C are actually stronger than P-C! The same could easily be said in the other way too! This, I think, is why we have to step-back and look at the bigger picture: the exact physical properties vary considerably from one compound to another and paint a landscape that says the issue is complicated. Perhaps, instead of it being a mere thermodynamic issue dealing with a comparison of the general bonding energies, it has more to do with the kinetic advantage of having enzymes equipped to slice the P-O-C rather than P-C. Of course, your mileage may vary depending on your specific examples.