Nowadays you can purchase pre checked fresh lettuce, and frozen checked veggies. What is more preferable - to check yourself or to purchase pre checked?
Halacha does not require us to check for bugs unless a product has a halachic certainty of having bugs (chazaka, which may require checking mideoraisa) or commonly has bugs (matzui, which requires checking miderabanan).
The best possible method to do a large amount of lettuce is to create a halachic certainty that there are no bugs (a chazaka) by checking 3 heads. If they are clean, the rest of the batch can be halachically assumed to be clean. (Heard from R' S. Eider)
Most of the hashgachas on the triple washed lettuce merely relied on the washing process and possibly spot checks. I can only assume that they held that (at least when pesticides are used), it is at best "matsui" and the triple wash with chemicals is assumed to release any remaining bugs.
Practically, I have found that fresh leaves that have been sprayed with pesticides are very clean. Though I check them anyway, I do so after rinsing with only water. I can go through a head in less than ten minutes. I have found a brand of organic leaves that still have hashgacha (not iceberg lettuce) but have stopped buying them because every container I bought had a bug on almost every leaf.
R' Heineman permitted plain frozen vegetables without hashgacha. I was told by a colleague that he did so after seeing the process in the factory. The vegetable would be spun and drained and spun again. If any bugs were found after the second spin, the batch would be tossed since if any bugs were found, people would stop buying the brand. I assume the heter is similar to the triple-wash above.
Consult your Rav if you should go by the triple-wash or frozen veggies. If you are using a hashgacha that is "machzik" their batches, there is no need to check leaves or veggies any more than you need to check a banana.
I know that R' Avraham Blumenkrantz zt"l wrote very sharply (in his annual Pesach guide) against what he called the "commercialization" of checking for bugs, the standards for which, he argued, are inadequate.
With that said, though, it may just depend on whether you have the necessary qualities (patience and sharpness of eyesight, among others) to do a proper job yourself. If you do, then indeed it's probably much better to do so rather than to rely on someone else's word. Otherwise, though, you're likely better off with the pre-checked vegetables, since then at least there's a reasonable chance that they are bug-free.
I would imagine both; buy pre-checked lettuce, then rinse and check them with a quick once over.