In Zechariah 14:16 the prophet is probably not referring to conversion in the sense of becoming Israelites, (or Jews already at that time). In this passage as in other similar passages the idea is that the nations will recognize the God of Israel as the true God, the only one worthy of worship. Conversion as we think of it today is not required.
The passover holiday is in fact two separate holiday's - the passover sacrifice and the feast of unleavened bread. The passover sacrifice is on the fourteenth of Nisan. The feast of unleavened bread is the following seven days. Participation in the passover sacrifice is limited, first to members of the Israelite community, in Exodus 12:43, and secondly by the requirement to be subscribed to a particular lamb together with a group (Tractate Pessahim 8:7). These requirements make the sacrifice, and indirectly the feast of unleavened bread inappropriate for universal participation.
There are no particular restrictions on participation in the feast of Tabernacles. In terms of sheer joy, it is the ultimate Israelite holiday, often referred to as simply "the holiday". So it is an appropriate time for universal participation.
Nota bene - Passover and Tabernacles are poles apart in the calendar, passover being at the beginning of spring and Tabernacles at the beginning of winter. They are also poles apart in the particular/universal themes of their celebration. In a similar way, the Day of Atonement and Purim are poles apart in calendar and theme. The Day of Atonement being a day of the spirit whereas Purim is definitely a day of the flesh. A similar duality with Weeks and Hanuccah with regard to celebration of the heavenly and earthly Temple service, though this particular duality is not mentioned much now after the row with the Saducees.