They are synonyms in nowadays Arabic (either Fusha or Accents), but In everydays life we use عندي more frequently. But if you want to use it in rhetoric context, then: عندي indicates possession, even if you do not have in your hand now. (Can be used if the thing is in your hand or not) لدي indicates possessing something right now. (Only used when you have it now)

The difference between the two sentences is when we say عندي we says about something we have it but we don't have it in the moment like ex: you talk with your friend and he asked you have you a dog? You will reply : عندي so we use عندي for speak about something we have it but isn't with us for moment or we have it in the past. But we use لدي When we have something and it's with us in the moment so we use لدي for present

لدي is the original arabic عندي modern arabic But both means i have

لدي فصحى و عندي عامية

عندى means I have it, maybe with me, or at any other place, but I have it and that's what it matters. لدى means I have it right here right now. عندي تفاح أخضر maybe here and maybe at home. لديّ تفاح أصفر I have it with me and ready to share. 😁😁