I'll give a brief overview based solely on MY experiences and ONLY SOLO Q.
Dropships - Teammates usually choose hot spots, and at least one of them dies within the first 10-20 seconds. Then the fun begins, a few minutes of trying to respawn them (usually the other team immediately pushes us, and we end the game).
Dropzone - Here we have more time to find weapons, heal, etc., which is great, BUT... if the first fight goes wrong and one of us dies, respawning them is very difficult because there are other teams everywhere around us that will kill us in the next few minutes.
In summary - both have their pros and cons, BUT solo Q is the most devastating, because with 93k kills and a K/D of 3.6, I can't play ranked games with randoms. The worst is when I get a duo on my team, they always play alone and don't look at me. Solo Q in this game has never been as bad as it has been over the past year.
As Hakis said - until Respawn improves the experience for solo q players - the player base will continue to shrink and people will not want to come back to Apex. Already, pubs, wildcards, and rankeds are dominated by 3stacks. When you play outside of peak hours, the game is absurdly frustrating.