I have the cuttlebug and love it. The platform folds up so it takes up less storage space than the BigShot. It will work with any of the embossing folders available, from any vendor. It comes with standard size plates. For the long folders, you need to get the longer plates. It will work with all of the dies except the very large ones.
No, you cannot make your own dies. The cricut is a lot more versatile, as you can vary the size of each of the images and manipulate them in many ways. The manual die cutters work with fixed size dies. If you want different sizes you would need to find sets that include multiple dies, such as the Spellbinders Nestabilities in geometric shapes. That can add up to a lot more money than a single cricut cartridge that includes dozens or hundreds of shapes, each of which can be resized.
You may want to get both the electronic and manual machines, as each has its pros and cons. I use my cuttlebug more frequently than the cricut because its so handy, and I love the embossing effect. There are a few combination embossing dies/folders you can get.