Here's a few more things to add to @fredley's answer.
Since the water is going to be in contact with the grounds for a longer time (1- using greater volume of water, and 2- Chemex filter will be slower) you're going to get more of the bitter notes that you get (in general) by using a longer brewing time. Acidity will be offset somewhat by the bitterness. I find Chemex to be like a filter-coffee version of the body of a French Press preparation, though with no sediment. Compared to the throughput of V60 filters, @fredley hit it on the nose.
Though you are asking about taste specifically, there are other factors.
Like @fredley said, the filter paper in Chemex is much thicker and water drains through it significantly more slowly. You'll probably want to use a coarser grind (and very even grind) than you would for V60 or Melitta-style filters. Fines are the enemy of Chemex, causing the filter to clog and welling (see this question about "welling up" in a Chemex for more on that). Certainly use the best burr grinder you can and don't delay in the pouring action.
Technique is "more important" (read as: "finicky") with Chemex, I think, than other pour-over systems. See preparation guides such as from Chemex itself, or Blue Bottle, or Stumptown, or search for others.