LEDE is basically an OpenWRT fork which is being actively developed. The biggest draw is that it's actively developed, and managed in a Linux-style package manager setup, rather than monolithic baked firmwares that you have to flash wholesale. Patching against things like KRACK was as simple as just invoking the package manager.
DD-WRT and Tomato are both old tried-and-true alternatives to vendor firmwares, and they require less tinkering to get into the state that you want, but they both tend to have weird crufty edge cases that never get properly fixed and don't seem to have any clear direction or leadership - they are both a hodgepodge of forks that you have to spend time digging through hundred-page forum threads to find information about. Development schedules are sporadic, and you often end up with dozens of potential builds in varying states of beta and testing which fix this or that but break this or that other thing. When they work, they're great, but my experience with LEDE has been consistently superior than my experience with DD-WRT or Tomato.
Just to be clear, OpenWRT isn't 100% abandoned, but it's basically just a handful of sporadic package version bumps and backported bug fixes, which might not ever make it into an official numbered release. If the counts on GitHub are accurate/comparable, LEDE has almost 2000 more commits than OpenWRT. The OpenWRT website also seems to be semi-abandoned (the front page has had a spam post on it for over a month; it looks like it was moved there accidentally by a moderator intending to move it to a "trash" subforum).
I naively bought the Linksys WRT 1900AC about when it released because it claimed dd-wrt support at release.
Then the dd-wrt folks mentioned that Linksys never actually gave them hardware ... and if I recall, hadn't really been included in the plans to support it at all.
So then I waited and found whenever I looked for the dd-wrt firmware, it always had lots of caveats and known issues.
I gave up. Shelved it and bought a pfsense box for the internet and use a Ubiquity wifi AP.
I ran openwrt and then lede on a wrt1900ac v2 for about 1.5 years until last week. Initially, stability was spotty, but the latest Lede images worked generally well. However, while vlans with Lede worked perfectly with my two TP-Link WDR3600s, the Lede ultimately had issues with it. I tried one last thing, probably bricked it, and that was the last straw...ordered three Unifi aps and couldn't be happier.
OpenWRT/LEDE is great assuming your device is well-supported and well-tested. Unfortunately, the wrt1900ac line was never as open as Linksys claimed it was, the LEDE devs didn't get the support they needed from Linksys when they needed it, and so certain things still don't seem to work.
LEDE has a very active anti-bufferbloat research people working with it.
LEDE has, in general, active, managed, and unified development. You'd have to hunt down a specific Tomato/DD version that works for you. Sometimes the latest version of DD/Tomato works, sometimes it doesn't. LEDE? Just download the latest stable release, done.
The big one for me is that LEDE uses a recent kernel. DD-WRT and Tomato use the kernel that was provided by the hardware vendor. They have an easier job to get things running because most hardware vendors have some crazy (perhaps binary only) kernel modules.
When buying hardware, look at the LEDE hardware support list. Recently I have bought a TL-WDR4300 (get right version) and a Buffalo Airstation N600 router. LEDE runs good on these and the router has enough flash and RAM. Running hardware vendor firmware is not good, IMHO.
I love my Tomato router, I'm on my second in about 7 years. Asus N66u I think. The first I bought and configured myself, which was a tiny bit of pain finding the right binary, etc. The router I'm using now I bought from FlashRouters.com at a fairly high margin above what I could buy the router alone, but they're fast and I trust them. I just recently bought a backup router from them too, and preconfigured it for minimal downtime should the current one break.
DD-WRT and Tomato are both old tried-and-true alternatives to vendor firmwares, and they require less tinkering to get into the state that you want, but they both tend to have weird crufty edge cases that never get properly fixed and don't seem to have any clear direction or leadership - they are both a hodgepodge of forks that you have to spend time digging through hundred-page forum threads to find information about. Development schedules are sporadic, and you often end up with dozens of potential builds in varying states of beta and testing which fix this or that but break this or that other thing. When they work, they're great, but my experience with LEDE has been consistently superior than my experience with DD-WRT or Tomato.