I do everything by hand, and I've infiltrated a couple of knitting groups with quilting. Here is what works for me. It's completely subjective, what doesn't work for me will be favourite for someone else.
1. I don't like EPP, I find that it's pointlessly slow and I'm much happier drawing my sewing lines straight onto the fabric, or making freezer paper templates if I'm using uneven shapes. I don't like whip-stitching either. Other people love it and find that they can whip-stitch faster than they can sew running stitch.
2. With the vast majority of my piecing, I press the seam straight after sewing it. You can't do this when you're out. Finger-pressing works for some people, but I find that it leads to inaccuracy for me.
3. There are a few shapes where you don't need to press as you go. I made a scrappy quilt out of lots of 30 degree diamonds, which I sewed into strips, and then I sewed the strips together. I didn't press the seams until I'd decided which strips went where and which way around they'd go. So this was relatively portable, I would decide on the order for a strip set and put it into a little sandwich bag, together with pincushion, needles, thread, scissors, a small plastic bowl to use as a bin, and an A4 cutting mat so that I had something to pin against. Still not the most perfect thing in terms of portability, there was pinning and sewing and I really needed a bit of table space to work at, at least for the pinning.
4. Quilting, on the other hand, requires much less Stuff, in my opinion. Though you're likely to be dealing with a bigger item, unless you deliberately choose a small quilt. On the other hand, it's all put together and secure, you just need your quilt, frame/hoop if you use one, and a small box containing needles, thread, scissors, and the aforementioned bin. You generally want to make sure the quilt is not big enough to trail on the floor, since public places rarely have a floor so clean you'd want to drag your quilt against it. Cushions are good for small projects, and an ideal size for travelling with.
Jinny Beyer is a professional quilter who does everything by hand, and she does most of it in "found moments" such as waiting rooms. She cuts up the fabric for her blocks, then puts a block's worth into a little plastic bag together with a small kit of needles, thread, scissors (possibly thread snips). This means that she has multiple sewing kits, but the ingredients are cheap enough, and she can stash them in various bags and cars and so forth, ready to go. She gets an amazing amount of work done this way. "Quiltmaking by Hand" is the book of hers I'd recommend if you decide you are going to try hand-piecing or hand-quilting.