It's still a crapshoot in terms of pricing and deliveries, doesn't matter whether it's Lazada or Shopee.
For instance, for DJI products, the promos on the DJI Official store in Shopee are better than Lazada. Meanwhile, for instruments and audio equipment, Lyric Philippines is cheaper in Lazada than Shopee (both official stores.)
For shipping, it really depends on who the logistics provider is. The in-house "express" option for both Lazada and shopee are terrible. GogoExpress needs to be avoided like the plague, while Ninjavan and J&T have historically been inconsistent.
In terms of UI and UX, Shopee is better, imho.