I usually don't push any particular product. After all, we may not always be cleaning & lubing at our own benches.
I usually suggest people consider the conditions where they're going to be carrying & using the pistols, and how often they're going to be going between cleanings.
I've had some oil-type lubes dry out, wick/run off and evaporate more quickly than I expected.
Greases will often remain where you put them, longer, being resistant to wicking & running. However, some are harder or softer than others. They can also sometimes require more attention and care in applying them (directly where you want them). Then, there's the risk of having them accumulate any sand, grit or debris and turning into an unintended, improvised lapping compound.
If an oil-type lube thins, wicks, runs off (under gravity) or dries too quickly, it may require more frequent reapplication than a good grease.
Using a separate products for cleaning & lubrication may, or may not, be something that suits someone's maintenance practices. Ditto using a combination CLP product.
Just depends.
Nothing wrong with considering using less toxic products, either, or something that smells less obnoxious. Read the labels.
I've tried all manner of products, from the days of the simple solvents & gun oil in JC Penney, Sears or Wards cleaning kits, to 3-in-1 oil or sewing machine oil ... and more of the ever newer products than I could hope to remember. I still sometimes surprise myself by finding some bottle, jar or tube of something tucked away in some old supplies that I'd forgotten I'd owned.
In answer to your specific question, though (in case you thought I'd forgot) ... Break-Free for more frequently cleaned & lubed guns, and grease for guns going longer between cleanings, or used in climates and conditions where moisture and temperature varies a lot (as long as sand isn't getting in the works).
I often find myself cleaning & lubing my own guns at the agency range, instead of my home bench. In that case, I often use either Break-Free (it's what we've got for CLP, coming in large jugs/bottles), or sometimes TW25B grease (one of 2 greases that's ordered at different times, by different people). If it's Break-Free, I'll probably end up checking to confirm its presence, and often reapplying it, within a month or two (or three, or so on). I tend to dislike the other grease for my own use simply because it's thicker and harder, making it more tedious to apply.
While I don't usually shill any specific products, I do tend to shy away from the latest flavor of wonder lube (or snake oil) being bandied about the internet, or using automotive products that haven't been specifically tested for firearms, meaning for 'open' use on equipment constantly being handled (and on exposed skin & clothing). Not saying it won't work, just don't like being a guinea pig (safety exposure) or smelling like an oil rack.
Lots of good quality products out to be found.
I think my bench and armorer kit presently has a varying combination of FP10, Break-Free, TW25B grease, Wilson Ultima grease (had it for years - makes me wonder if it's somehow self-replenishing
) ... and some really slippery stuff marketed under the S&W name (some shimmery, white liquid goo that's more slippery than duck snot and doesn't smell like anything I've ever before used). Other stuff in cabinets and downstairs.
The gun companies have usually avoided making specific recommendations in my armorer classes ... except for SIG, where the instructor said the company really liked TW25B. They must, because the last time I was using some NIB SIG's, they'd applied enough of it to each pistol to lubricate a dozen or more guns.
The other classes have generally recommended using any of the modern high quality products specifically sold for use on firearms, as well as considering any specific operating and/or environmental conditions in which duty weapons will be used (leaving it up to armorers to make their own informed decisions).
