Reaper has InputFX which actually do get recorded.
You get to pick, of course, and it's all about how you want to work. There's something to be said for just making a decision and committing to a sound. Recording Input FX is very much the same as sticking a mic in front of an amp. You get what you get, and if you need to change it later, your only tools are "fix it in the mix" things like EQ, compression. If what you really need is to change a setting on the amp itself, you have to retake the whole thing. It's a valid, kind of old school approach, but it does require that you have a real good idea of what you're shooting for, and if you're doing it all in overdubs, it requires that you be able to imagine how the sound you're recording now will fit in with things you'll record later. That ain't easy, but it is a good skill to have.
That said, I still don't see a real point in recording that way. It mostly defeats the purpose of the non-destructive workflow of any decent modern DAW. I can just as easily dial in an amp sim on a regular insert and then never touch it again. Heck, I could even render the FX right away after recording, but the original clean input is still there somewhere in case I want/need to go back to it.
One important thing to keep in mind is that when comping guitar tracks - whether you want to record multiple takes and pick the best parts of each, or even just punch in over a brief mistake, or whatever - it is often a lot easier to make it seamless and transparent when you can do it before the FX. Especially if you've got other effects before the amp like delays or modulations or reverbs, but even ringing strings or sustained notes. It's more forgiving in a lot of ways, but also just gives you finer control.
Edit - ^^^ The above actually applies to most "editing" procedures you might do: Timing or pitch correction, etc...
Can't say for sure why one way would sound louder than another. There's no good reason that should be true. Must be something simple and kind of silly, but I'd have to know a bit more about exactly what's going on to try to diagnose.