What they share
Both trace to the Hebrew Elisheva, meaning 'God is my oath'. Both have been in English use for centuries. Both work beautifully across formal and informal settings. Both pair easily with classic English middle names.
Pick Eliza if…
Pick Eliza if you want the shorter, brighter, more immediate version. Eliza has a distinct, playful energy and does not typically get further shortened; it is already its own short form.
Pick Elizabeth if…
Pick Elizabeth if you want the deep classic with built-in optionality. Elizabeth gives you Eliza, Ellie, Liz, Lizzie, Beth, Betty, and more. Few names offer that range.
Elizabeth is the ultimate 'grow into anything' name. Eliza is a fully-formed choice in its own right, especially if you want something ending in a vowel. Either lands well; the nickname question decides.