Lutron is probably the best in the world at switch technology, whether they are networked or not networked. They hold a bunch of patents, use proprietary methods, and offer many features that other brands don’t have. But there’s no direct integration with SmartThings. Anyway, it’s not surprising if you find the other brands don’t have all the features of a Lutron device.
That said, there is a pretty wide variance in what features different Z wave switch manufacturer offer. Industry definitely has a good/better/best model, with GE being in the lowest tier. They are value switches. Lower prices, shorter warranties, and fewer features. Good enough for many projects, but you won’t find advanced features on them.
Double Tap
Double tap is tricky. Many Z wave switches do offer this in a local installation, but once you add use a cloud architecture as SmartThings does the problem is the lag time in transmitting the commands makes it very hard to do the precise timing that most double tap options require. There are a couple of custom Smart apps that you can read about in the forum that used to be very popular and did work for double tap with the GE switches, but these stopped working a few months ago for many people after a platform change.
As it happens, Homeseer just released a new line of Z wave switches last month that do have both double tap and triple tap options. Instead of trying to repeat commands to the hub, these switches capture the tap pattern at the physical switch and then send a different code to the hub for different patterns using the “central scene” zwave command set. Some community members have them and they reportedly work well. I’m honestly not sure whether they have the other features you asked about or not.
Many features, much higher cost
With the exception of double tap, the two switch lines that fall into the “best” category (but also cost much more than GE switches) are the Cooper aspire line and the Leviton Vizia high end models. These offer many additional features, like a panic mode where you can flash all the lights, various kinds of ramp rate options, etc. you just have to look at each model to see what it offers. The Cooper has a five year warranty, which is reflective of its engineering quality.
Both these lines are widely available from places that sell Z wave devices, but again, the price is going to be much higher than the GE price.
The GE are definitely good switches – – they just aren’t “best” switches. And Lutron is the best of the best. So it’s not surprising if GE falls short by comparison. 
I will add a couple of links in a minute on features and sources:
Features by device class (switches are after sensors):
Finding suppliers: