DISCLAIMER: I bought both sets of pencils myself, so nothing about this review is biased (it never is anyway!) or influenced by anything else.
Both are good at blending and shading, but there are some quite obvious differences. First of all, Prismacolor are prone to developing 'wax bloom' over time, which is a milky film that appears on the colour after a while. It happens due to a layer of wax rising to the surface when exposed to air. Light swiping with a cloth or cotton wool can get rid of the bloom, and spraying with fixtative can prevent it, but this can sometimes lift off pigment as well so it is a point to be noted.
I used two colours to achieve this blend, and tried to use similar shades to give as close a comparison as I could. I've learnt that the Polys can take a battering when it comes to adding layers, whereas the Prismas become speckled with dark spots quite quickly. This is probably down to the wax in the pencil, as too many coatings cause the wax to dull to black and go fuzzy. The Polys leave slightly noticeable lines but this is down to the technique used- if you 'scrobbled' the strokes you'd have a much smoother finish. Overall I found it easier to see a gradient with the Polys than the Prismas,even though the shades of colour were quite vastly different.
When using light strokes, Prismas leave a lot more white space than the Polys, so definitely need more layers to give a solid colour on the page. When it comes to hard pressure and layering, they're not too dissimilar. The only real difference is that nasty dark haze that appears over the Prismas with too many layers. I think I got the amount just right on the lower left box, as it does actually look smoother than the Polys in that example. Hmm.
When using the white pencil to blend and combine two different shades, the Prisma white adds on a very thick and cloudy layer which gives an ombre effect and almost obscures the colours behind. The Poly white is very hard and doesn't make too much of a difference. I'm undecided on which I like best!
With Polychromos the whole pencil feels stronger, weightier, which probably has something to do with the SV (secure-all) bonding. This is where the whole of the lead is glued to the Cedar wood casing of the pencil, meaning the lead is strengthened and can sharpen to a finer point. If the tip of a Polychromos pencil breaks, it is only the tip that is shattered, not the whole column of lead. The same cannot be said for Prismas, which unfortunately have a track record for splintering and fragmenting with ease. Apparently when Prismas used to be made in the US, the quality was much higher.
As I said I haven't had any breakages yet, but with the cheap feel of the pencil and the softness of the lead, I think it's only a matter of time. I'm very cautious every time I use them, as they feel so frail and insubstantial in my hand.
Thanks for sticking with me through this beast of a review and I hope you've enjoyed it! Any questions please ask and I'll do my best to answer.