I've done both in the last couple of years. Both are basically similar, a low fat, reduced sugar diet.
(Assuming WW hasn't changed since I quit 18 months ago), WW has two basic options - counting points or 'filling and healthy'. The points one, you count everything you eat based on its calorie/carb/fat value (all calculated for you). Filling and healthy certain foods are free or allowed, you count the others. You get a certain number of points per day and additional ones per week (you can top up any day) and can earn exercise points.
Slimming world is very similar to the filling and healthy. Basic principle with SW is you eat one protein portion a day and one fibre. You eat 1/3 'speed' food with each meal (certain fruits and veg) to fill you up. You can have up to 15 'syns' (calculated points) per day. There's a debate if you can save syns and use them another day. (I tend not to do this). There's also an SP plan which is essentially low carb.
Meetings are quite different. WW you weigh in then sit and listen to the group leader teaching from a set programme from head office. SW you weigh in then have 'image therapy' where you may have a theme but the consultant goes round each member to discuss their progress and give them support (weekly and total weight loss is discussed, never heard them say what you actually weigh).
Personally I found the WW format very cringey! But some people hate their weight loss being discussed and prefer and structured format and contributing where they want to.
Having tried both, I've had a lot more success with SW. I lost 1.5 stone in 6 months with WW. Then I plateaued for 6 months, then I gained 1/2 stone in 6 months! With SW I've lost 2st 3lb in 4 months. I found myself being too restrictive with WW then bingeing. With SW I am eating loads more fresh fruit and veg and limiting my bread intake which really help me lose weight.
Hope that's clear enough! Ultimately it's your choice and what you think will suit you BESH.