They are "spiritual sequels" to each other but their only true connection is that they were developed by mostly the same team.

Xenogears was the original game (it was originally intended to be a Chrono Trigger sequel, hence several similarities to CT are seen throughout the game)) and due to some bad handling was rushed and released early. Perfect Works (think the Xenogears Ultimania) was released to clear up some of the confusion and expanded the world presenting a timeline that spanned thousands of years. The team left Square and formed Monolith Soft so they can do the Xeno story right but due to Square owning the original rights, the Saga series only alludes to Gears in more of a fanservice way than being a true prequel.

Still Saga has several visual and scenarios that are related to the Gears world. The main theme central to each is the Zohar which exists in both games, though its more prominently shown in Saga than in Gears. Beyond that the rest are more just simple fan service like the Uzuki name, as well as the name of several locations only mentioned in the Perfect Works timeline, and several of the bosses are visual and downright literal fanservice.

Part of the problem with connecting them is that Saga technically begins at the very start of the timeline presented in the Perfect Works book, which starts the idea they might be directly connected. Several places from that timeline are also mentioned but it should be noted that Perfect Works only describes this date in a simple paragraph and makes no mentions of Gnosis or what not. In fact the few things that do appear in Saga that are part of the Gears timeline are presented differently and ultimately resolve themselves within the Saga story whereas they are of great importance in Gears time and will not be resolved for several millennium. By Episode 3 its kinda of obvious that Saga is going in a different direction that is similar to PW but not verbatim but that was the teams goal. They said from the beginning of the Saga project that Saga was not going to be simply a direct telling of the Gears plot but rather a re-imagining.

So the question is now this: Should you play Xenogears despite it not being connected to Saga?

Yes... Oh god yes, this game was incredibly well beyond its time and put just about everything to shame at the time in terms of story and complexity. Gears is an excellent game on its own but I feel playing through Gears will allow you to appreciate Saga more as you will be able to enjoy all the in-jokes in the Saga series that only Gears fans would notice. Its plot and even the philosophy its based around is very different but it is definetly a Xeno game. Its definetly worth checking out if only to see the game that formed the mythology for the Saga series.