There have been some great comments on the issue thus far, so I'll try to not be redundant. But to answer your question about Axis or Gibson, a question that needs to be answered is what is the reason for the 2nd guitar? Without knowing the reason for the axe no. 2, we can only make shots in the dark. So here I go...
A second Axis doesn't make sense unless you need it as a backup and you want your backup to be as close as possible to your existing Axis--unless your new Axis is different from the first. MM90 vs Humbucker. Hardtail vs Floyd. You get the picture.
If you want a Les Paul because you want that sound, there is probably no substitute. It's the same with Marshall amplifiers, for example. If you want that Marshall sound, that's what you'll have to get. Other guitars can come close, but none will nail it.
Now, if you want something that sounds close to a Les Paul but be within the EBMM line, I think your best bet will be a 20th Anniversary Silhouette. If you can't find one, then your next best will be a regular Silhouette or a Silhouette Special, depending on what kind of pickup you like next to the neck.
Others have talked about how an Axis compares to a Les Paul, so here I will pile on to add that the Axis "feels" better and "plays" better...but that is subjective. I've a friend who loves Les Pauls, their overall feel, and the shorter scale length; the Axis doesn't do it for him. The other difference would be in the sound. The Axis pickups have a more "modern" feel, a beefier sound. ("Modern" being more 80s vs. "classic", which I guess would be more 60s or 70s.) The Les Paul will have a bit more clarity and not as much balls, if you'll pardon the pun. I've not played a Les Paul much, but that's my take on it.
You already know how great the Axis is. If you're gunning for a Les Paul for guitar no. 2, I think the best advice I or anyone could give, however, would be to try one out before you buy. It is quite different from the Axis.
Good luck! And please let us know how it goes.
I have a Axis ss and I think it's awesome!! but now I am looking for a 2nd guitar.I was thinking maybe a Gibson les paul(never own one before) or a 2nd Axis.
I play mostly 80's Rock,how does the Axis compair to a Gibson LP?