I don't play on 888, but I almost exclusively play all poker sites throught the client on my laptop. If I were you, I would download and try both! Good luck!
Download the Windows version and mobile version so in case your playing only 1-2 table you can switch to mobile Apps easily if you need to play on the go.
I think the app is a greater choice, when im playing , i sometimes do some researches or listen to music when im playing and i think if i played on browser it could be a little messy
I prefer to download from the site because I usually play several tables at the same time and I don't like to do that in the app (actually I don't even know if it's possible).