Been running these by dual-boxing with 2 accounts. There is often competition for the Emerging Conduits, but very rarely for the Minor Conduits. Naturally the Emerging Conduit is easier and therefore more accessible by wider range of players, but in my experience it is also better value for your time (the almighty ISK/h).
I think the rewards for Minor Conduits should be better (or worse for the Emerging ones, but that is likely not a popular opinion).
I takes me an average of 7,5 minutes between completing Emerging conduits with full loot and salvage (i.e. 8 sites per hour). I get 9M isk as a payout from DED and then an average of 10M in loot+salvage. This gives me about 150Misk/h.
For Minor Conduits the completion time is close to 20 minutes, which is then only 3 sites per hour. I use medium weapons, so a lot of the time is spent on killing the Leshak orbiting at 40km. The site gives me 30M isk from DED, but the loot is surprisingly about the same 10M as the emerging conduit. The result is only 120Misk/h. The sites become even less attractive, if I factor in that there is a real risk of losing my ship when messing up in Minor Conduit, something that is very unlikely in Emerging Conduit.