yeah propecia = finasteride (propecia = merck's product name, finasteride is the actual drug)
DHT naturally inhibits estrogen, and less test being converted to DHT also means more free test to aromatise to estrogen. This doesn't necessarily mean you'll suffer any estrogen related sides, but it does mean there's a good chance your estrogen levels will be higher.
In my completely unqualified and unimportant opinion, taking an estrogen modulator is a good idea - not high levels of hardcore suicide inhibitors or anything, you do want some estrogen on a long term basis! More like Resveratrol and/or I3C or DIM... I think Primordial performance's sustain alpha is a good one for it too, although using that on a long term basis can be pretty pricey.
dutasteride is fin's evil twin, it inhibits both type I and Type II, and thus brings total DHT levels way lower. In theory this might make for a more powerful hairloss drug, but anecdotally I've seen people claim fin worked better for them, some claim dut worked better, some claim dut caused it to get worse, some claim fin caused it to get worse. Basically though any side effects from dut are going to be magnified versions of fin because it essentially gets rid of far more DHT. I suspect a hyperandrogenocity response is more likely with dut as well, although that's just from logic rather than any evidence, could explain why some people claim to experience "never ending shedding" though. It also has a much longer time to return dht levels to normal. If you quit fin your DHT shoul return to normal within 1 - 2 weeks, dut is over a month.
Personally I don't think dut is worth the risk, there's not even any evidence showing it to be any better against hairloss. I'm not entirely sure it was ever even tested for that purpose, i think people just started using it as a logical extension of finasteride.