I wouldn't recommend anyone put serious time into most console Bethesda games. They are notoriously unstable. At least on PC if something happens and you get stuck, you can use the console commands to fix things.
I played FO3 on the PS3 back when it was still relevant, and the constant crashing later on in my save made it pretty much unplayable. It's not related to specific DLC's or anything, it's just the save file as people have said. I did the whole alien DLC without crashing during the whole thing. Eventually save bloat happened, and I couldn't play for more than 5-10 minutes without crashing. There's no fixing it once it happens.
Save yourself some trouble and just play it on PC. You can probably lower the settings as others have said and make it a playable PS1 version of FO3. I did similar with Oblivion when it came out, and they use the same engine.