Both sentences are technically correct. However, no native speaker would ever say 'I have got much money'. In natural, modern English, 'much' is mainly used in questions and in negative statements. 'Much' is never used in this way in an informal-style statement of this type. 'I've got a lot of money' is a natural statement. Also, note that we don't usually say 'I have got...', unless we are emphasising or contradicting. The usual forms are either 'I have ..' or 'I've got..'

"I have got a lot of money" is correct. we generally use the word 'much' in the negative E.g ( "I don't have much money on me".) but you can't say "I have much money".

We say" I have a lot of money" ,we never say I have much money. Many is used with a plural, I have many problems. A lot of is used with singular nouns, I have a lot of homework. I have a lot of bread. You can also use a lot of with plural nouns. I have a lot of problems. Much is used for negatives in the singular, I don't have much hope, I don't have much luck. For plurals use many, I don't have many friends!

Well, first of all the two phrases are different so, I don't think comparing them is the right thing to do. Secondly, they are both correct though, in the first after using "much money" I'd go further "saying in the pocket", "on me/wih me", "in the kitty", "in my bank account", etc. Regarding the second, here we are dealing with a statement and it could stand on its own perfectly well.