Mke your purchase on what it is you want to hear. An LP and an ES do not sound alike. You could say similar in that they both have humbuckers but they are different animals.
I find the ES to be a bit more mellow and the LP was more amenable to harder tones. Not that you can't cross over and make an LP mellow or kick it out with an ES but it's more the point of where the guitar is at home in as far as tone. If you're playing jazz, an ES might be better because it will better get to those tones most used with the genre. That kind of thing...
Granted, when I had an LP it was a while back and the LP was a 68 Deluxe (was reconfigured with standard HB pick ups by the time I got it)...so it's been a while. Though I own the ES currently.
I wouldn't buy on what is the best purchase decision but what best suits what you wish to play.