Either method is fine so it becomes a matter of taste and skill.
The first method is the overhang bullnose style, which is the most common. I believe you are using the Trex style grooved decking that utilizes the invisible clips. The grooved boards are definitely not what you want to use for the bullnose or any outside edge, as the grooves will show. You need the standard radius edge boards for those exposed pieces. They may be in stock at your supplier. One major advantage is that two pieces usually makes a perfect 11 inch tread and installation is very easy and any mitered corners fit well together. Don't forget to use some glue and thin SS finish screws to keep corners tight.
The second method of flush mitered edges is very difficult to build correctly. All edges of the treads and risers should be rip mitered. Exposed ripped edges look terrible. If you have ever tried to rip long lengths of Trex, you will find it is a lot more difficult than it looks. Cut edges of Trex can be very rough if you don't use a sharp 60 to 80 tooth blade, not at all like cutting wood with an 80 tooth blade to get a smooth edge. Trex is unforgiving if you wobble a little or pause during the feed through the saw. Trex does not sand well at all, so any imperfections cannot easily be sanded out without harming the sheen or texture of the finished, exposed side of the Trex. Long mitered edges can be very difficult to make fit tightly. You will have to glue and use lots of finish nails to keep the joint tight and free of gaps. Another consideration is that because Trex is fairly soft, mitered corners are susceptible to chipping and denting.
I think you are seeing that my opinion is to use the bullnose method over the flush method when using Trex or any composite, flexible decking.