It depends greatly on how you estimate those externalized costs.
A plastic soft-drink bottle https://www.polisanhellas.com/products-pet-preform.html is about 30 grams of extremely chemically inert material, produced for a tiny energy cost from about 30 grams of crude oil, that goes to a landfill and stays there for, probably, millennia. So a single barrel of oil makes about 5,000 plastic bottles. Each bottle embodies about 1200 kJ of energy from oil that would otherwise have been burned. So whatever the externalized costs of drilling, refining, and shipping a barrel of oil are, it's about a five-thousandth of that. If you incinerate the bottle in the end, you get that saved-up energy back, at the risk of producing pollution from other things in the furnace.
Of course, blow-molding the bottle takes energy; you have to heat those 30 g of plastic up to 125°, but that only takes about another 4.5 kJ per bottle. Another similar amount was spent to injection-mold the preform. The actual work of blowing is even less, under 0.1 kJ. Similarly for shipping, molding machine operation, machine maintenance, catalysts, and so on.
(A potential hole in this analysis is that I don't really know the energy costs of the whole terephthalic acid synthesis and polymerization process. They can't be enormously higher than the cost of molding, but they might be a lot lower or a little higher.)
Contrast that with washing a glass bottle. You can't really wash a 500-mℓ glass bottle with less than about a liter of water, and to sterilize it you need that water to be at least 60°, preferably more like 90°. Heating water from 25° to 60° takes 35 calories per gram; at 4.2 J/cal, that's 150 kJ.
(I think in actual fact the energy to reuse a glass bottle is about an order of magnitude higher than this.)
You also have to take into account the energy to make the glass bottle: you're heating 500 grams of raw materials (or maybe cullet) up past, typically, 1200°, which takes maybe 700 kJ, depending on the materials' specific heats and enthalpies of fusion. This gets amortized over the number of reuses of the bottle.
What about disposal? Proper disposal of a 500-gram glass bottle uses 15 times as much landfill space as a 30-gram plastic bottle (just as it costs 15 times as much to ship) but in any case there is no shortage of landfill space, and neither type of bottle occupies an appreciable percentage of existing landfills. Improper disposal for glass bottles is much worse, as you know if you've ever stepped on a broken glass bottle underwater at the beach. Chemically, both materials are very inert and nontoxic. (Microplastics are almost entirely from washing synthetic fibers, not from plastic bottles.)
So, making a plastic bottle takes on the order of 10 kJ of energy, while washing a glass bottle for reuse takes more like 150 kJ, and similarly shipping glass around externalizes 15× as much of each cost. Neither one has significant disposal externalities, except in the rare case of improper disposal, in which case broken glass is dangerous.
The crucial question, then, is how you weight the raw-material extraction externalities for the plastic bottle, and whether you incinerate it; because if drilling, refining, and shipping oil is the most significant externality (oil spills, bribing Nigerian officials, arresting Native American protestors asserting a sovereign right to block the Keystone pipeline, US invasions of Iraq), then the plastic bottle is about 7× worse. Unless you incinerate it instead of burying it in a landfill, in which case suddenly its oil consumption drops to zero, making it much better again. On the other hand, if the most significant externality is something related to burning oil or other fuels, like global warming, washing the glass bottle is 15× worse than throwing it out and replacing it with a plastic bottle. Unless your hot-water heater is solar or geothermal. Then again, you can run a blow-molding plant on solar energy, too.
(There are other questions of pollution; both glassmaking and PET-making can produce pollution, but it's not intrinsic to either process, so which process produces more pollution is largely a matter of how mismanaged it is. However, by virtue of dealing with 15× larger quantities of material, glassmaking is at a disadvantage here.)