I first used DD-WRT on the venerable WRT-54G. Linksys had moved on to other products and the stock firmware had become stale and insecure. The exciting thing about DD-WRT was that it did unleash the power hidden in that old router and enabled it to do things that the stock firmware could never do. (I later switched to using Tomato instead but that's another story.)
My preference is to use the stock firmware (when I can) simply because it's supported. I don't care about the Linksys smartphone app, nor would I ever use Smart Wi-Fi or any cloud management apps. As a former CCIE, I don't even care about a fancy web UI for configuration. All I want is good software running on good hardware. At some point, vendors will stop supporting their products and when that happens, it's nice to have robust, secure, third-party firmware to fall back on.
Normally I would be excited by 3rd-party firmware for the latest WRT-series but Linksys has failed us time and time again by advertising these routers as "open-source ready" but they have yet to deliver the all-important (and stable) open-source drivers.
I have mixed feelings about DD-WRT. On the plus side, it's a complete integrated product; there are no extra software packages to manage or upgrade. Many like their web UI. If you happen to have the same hardware that the project leads are using, you'll probably have a great experience that's better than that vendor's stock firmware. For any other products, DD-WRT is in a perpetual beta; one week it may work great for your config but you may not be so lucky with the next release.
My 3rd-party firmware of choice right now is OpenWrt/LEDE. I used to like the classic OpwnWrt but the project had fallen into disarray. LEDE fixed that, updated the base platform and packages, and started building Stable releases. After re-merging with OpenWrt, we've haven't seen a new release in a while. However, community builders, such as davidc502, have produced stable builds for the Linksys WRT routers (based the Development branch) with newer, more secure and more functional kernels and better device drivers. It also looks like they may have also finally found a pretty stable Wi-Fi driver for the WRT3200ACM; missing some features from the stock driver but stable. I also like the fact the the base OpenWrt image has the essential features needed by 90% of the people out there, and that it can be augmented by instaling additional packages to meet the needs of the remaining 10%. I'm looking forward to the next official Stable release from the re-born OpenWrt team.
I *do* think that 3rd party builds like DD-WRT and OpenWrt are not just useful but essential. Each have their own place depending on the wants and needs of the end user.