If you haven't seen The Honeymoon Killers (1970), I feel it should be recommended to watch that before Deep Crimson. Its not necessary of course but one might appreciate both films a little more when the original is experienced first, generally speaking. I also think Deep Crimson is a tad better than the 1970 original, but they're pretty close and each has its pros over the other depending on your perspective. Without mentioning the plot details, I'll focus on style first. Honeymoon Killers was shot in black and white while giving off an almost amateur film/documentary vibe which gives it a gritty edge. It also seemed to mostly be shot in small interior spaces, giving a claustrophobic feel.
Crimson might have a more typical feel throughout the first three quarters, but its still beautifully shot, especially the fourth act which takes advantage of wide open spaces. My memory might have failed me but I think Deep Crimson did a better job with the psychological aspects of the characters. Both films are dark in subject but Crimson left me with a depressed feeling, like I shouldn't have seen what I just saw.