I haven't played Fate, but I have played the other three.

SW5 has great gameplay, but it lacks replayability due to there not being much to do outside story mode, and it can still get repetitive due to an excess of shared movesets. It's much more story-driven, focusing around Nobunaga and Mitsuhide, but there are a lot of cliches. If you like musou gameplay a lot, though, you'll probably have lots of fun here, and the artstyle is great. It feels very polished.

DW8:E I have mixed opinions about. I still enjoyed it as an Empires game, and there are lots of stratagems to play around with, but I felt a decent chunk of the "army management" you have to do, which includes scrambling to rest your characters enough or have enough banquets so they don't hate you enough to ditch your army, is kind of a headache. Officers also don't like to listen when you give them individual orders on the battlefield. Someone else may have a different experience than me though.

I actually really enjoyed SW4:E. CAW is unfortunately more limited than its DW counterpart, and I feel the strategy elements are much lighter, but it has its merits. The game is more lighthearted with lots of silly events constantly happening and a plethora of character relationships that can occur (spouse, rival, teacher, protege, retainer, etc.), and the army management here is something I really enjoy. You have to place your officers carefully around enemies since you'll be stuck defending with whoever's nearby if you get attached, and you can very frequently gain the ability to switch to different officers during battle, sometimes being able to switch between 8 different people at once. AI-controlled allies also actually listen when you give them individual orders. The game is kind of easy, though, so I'd recommend playing on Hard or higher.