It's a great question! The old Book of Common Prayer in the US (1928) had a somewhat different tone and feel to it. The language sounded more "King James," and thus worship contained a certain formality. The current (1979) BCP did a lot of updating to the liturgy, and Rite II puts it in the common vernacular. Rite I retains the older language feel for churches that did not want to lose that aspect of worship. Rite I is not exactly the same as 1928, but it's "in the ballpark."

A few of the responses in Rite I are different than they are in II (such as "and with thy spirit" instead of "and also with you"), and there aren't as many Eucharistic prayers. There's also a Rite I version of Morning Prayer and Evening Prayer.
Interestingly, having grown up in
extremely informal and (I hate to say it) shallow churches, even Rite II seemed quite formal to me when I first heard it. The parish I attend now does Rite I services on Sunday mornings. I love it. It has a certain timelessness to it. I try to avoid the inevitable debates that people engage in over the Rites, but I definitely like Rite I. Now they do have a Wednesday noon communion service here which is Rite II, and the Bishop always wants to do Rite II when he's here, so they're not hardline about it. But they really emphasize history and old musical works and so forth, so Rite I captures the feel of how they want to worship!