So this isn't something i just pulled out of nowhere. It's something I've felt strongly about since i finished Brotherhood for the first time many years ago.
Brotherhood can be seen as more of a soft reboot and less of a hard one in the right context. I know that Brotherhood is canonical to the manga whereas 03 had to go It's own way once it caught up to the books but hear me out here as nothing I'm about to say clashes with either of those facts.
A huge part of the story of 03 revolves around the concept of a parallel world, a concept similar to the multiverse. By the end of the series it's discovered that the FMA world is a parallel world to our own real world history, meaning that Amestris for the brunt of the main story is a parallel/alternate reality version of pre-WWII central Europe/Germany.
In this light, you can essentially view the continuing layers of parallel realities to be adjacent to one another metaphorically, with one on either side of the reality in question. By this logic, the two FMA series reference 4 distinct realities.
Reality 1: Our real world reality. Unaltered by the actions of alchemists from other worlds and true to history.
Reality 2: A version of our real world history that was affected by the actions of alchemists from other realities as seen in FMA 2003.
Reality 3: The FMA 2003 continuity version of Earth as seen and told in that series.
Reality 4: The FMA Brotherhood continuity version of Earth as seen and told in that series.
I find these layers make the overarching story all the more interesting. They even reference real-world ideologies like Christianity, essentially being an archaic/extinct religion in the lore of FMA 03. The series is rich with connections that make it strikingly similar to Brotherhood, but also unique and deeply connected to post-WWI industrial Europe.
How these facets enhance the experience of Brotherhood is more related to how FMA 03 and FMA Brotherhood each end. FMA 03 ends with Al choosing to remain trapped without Alchemy with Ed in the reality Ed had been living in since his disappearance from the 03 timeline years prior. This is an extremely sad ending because even though it's bittersweet to a degree with the brothers finally being reunited, it also means they'll permanently be cut off from all their closest friends and family. Winry, Pinako, Mustang, Armstrong, and so many others they'll never see again, but it's Winry, especially that makes it so bittersweet. Brotherhood ends with truth/god essentially confirming the reality of equivalent exchange, allowing Edward to trade his door of truth and therfor usage of alchemy for Al's body. Both series end with Edward losing his ability to transmute, but only one ends with him losing Winry. So, in the happier ending, Al gets to keep his alchemy, and they both get to keep the people they love in their lives.
By watching FMA 03 first, you get a deeply grounded system of connections between our real world history and the world of FMA. Then it ends with a very bittersweet moment, leaving you wanting more for Winry and the Brothers Elric while also making you just happy to see the Brothers reuinited. It also sets you up to view FMA Brotherhood through the lens of it being the next and final reailty for these characters. Experiencing these things before you watch Brotherhood makes learning the grandiose and truly happy ending of that series all the more meaningful. It makes Ed and Winry's ending especially and incredibly more impacful, emotional, and rewarding. Watching FMA 2003 after Brotherhood or never seeing it at all would be a true shame, i feel like, despite most fans agreeing that Brotherhood is the better series. I feel like more fans should recommend them both as one whole thing rather than try to put one above the other. They compliment one another enormously.