Haken

What I love about Haken is they take the counterpoint complexity of Gentle Giant and make it heavier and simultaneously more accessible. I've heard few others do that too, my favorite being "Author of Confusion" by Neal Morse. If you dig the songs "Cockroach King" and "Somebody" off The Mountain, check these I've found:

Edited by Friday13th - January 14 2015 at 14:06

You should try To-Mera, the other band of Tom MacLean and Richard Henshell, Delusions and Exile being the best places to start. IMO they're the better band as they're far more unique. 

Haken is amazing band, I have all their albums and two of them on vinyl, The Mountain and the recent EP Restoration, which are songs from their original debut but re-recorded since most current band members are new.

I'd finally discovered Visions from them recently. I've had The Mountain since it came out (because there was so much hype leading up to its release), and love that album, but I'm stunned with myself for not pursuing their previous albums earlier. I've recently purchased Aquarius, and will be getting that one in soon. I'm very much looking forward to their next release.

I haven't heard much Beardfish, but I'd toss their name in the mix. Their music is a tad less grandiose and a little more eclectic. Also their lyrics are less philosophical and more whimsical (reminiscent of Zappa in places). But in terms of heaviness, they're right there with Haken. Sleeping in Traffic, Part Two is definitely the place to start with them, from what I've heard.

Ah, they were all the rage up to the end of 2013 around here. The Mountain is perfect modern heavy prog by way of the Giant.