The G604 has a very typical right-handed ergonomic design: a centered hump that slopes down organically towards the front and back; a raised left side; the sides being curved inwards to create natural resting places for one's fingers. What sets the shape of the G604 apart from others are two things: one, the lack of a front or back flare; two, the overall bulkiness of the mouse body. This and the above average length make the G604 most suitable for palm grip and bigger hands. The only somewhat fancy design element is the raised lip on the right side, which is a rather dubious design choice. It doesn't accommodate the way hands are shaped to any substantial degree, but, rather, gets in the way of one's pinky no matter the grip style. Both main buttons feature subtle comfort grooves.
As for grip styles, I'd say the G604 mostly suits palm and (to a lesser degree) claw grip. It's a large mouse with a bulky body and fairly pronounced hump, which means it is better for larger hands. For reference, my hands are 19 cm long and 10 cm wide, and I found the G604 quite comfortable in claw grip.
Dimensions
This table includes the dimensions of the Logitech G604 and several other right-handed ergonomic mice. "Front height" denotes the distance between the base and the main buttons. Measurements with two decimals have been taken with a caliper, while those with one decimal have been taken with a ruler. For a full list of all measurements taken, please refer to this sheet compiled by an esteemed community member.
Logitech G604 Dimensions
G604
Scimitar RGB Elite
Basilisk
G402
Base Length
12.96 cm
10.7 cm
11.2 cm
11.5 cm
Length including overhang
12.96 cm
11.80 cm
12.2 cm
13.3 cm
Front Height (lowest point)
0.9 cm
1.8 cm
0.8 cm
1.1 cm
Height (highest point)
4.38 cm
4.20 cm
4.17 cm
4.05 cm
Front Width (widest point)
5.77 cm
6.65 cm
5.91 cm
5.58 cm
Back Width (widest point)
6.08 cm
6.89 cm
6.23 cm
5.54 cm
Grip Width (narrowest point)
6.00 cm
7.10 cm
6.05 cm
6.11 cm
Here are some comparison shots with each of the measured mice: