Do they have the same meaning ? If so, could anyone give any more synonyms of the two?
Thanks
‘Generally’ doesn’t sound specific to me, but ‘broadly’ does 
I know this is not an answer but it is a kind of subscription to this post so that I could follow up on the answers given.
They can in some contexts.
generally - Without reference to particular instances or details; not specifically: generally speaking.
thefreedictionary.com/generally+
broadly speaking - without regard to specific details or exceptions; “he interprets the law broadly”
thefreedictionary.com/broadly+speaking
Citing few examples –
Generally speaking, grammar does not appear to be a popular subject.
Broadly speaking, parents whose children were not at grammar schools felt ill-treated.
Can we say that –
We use ‘broadly speaking’ especially when we have analysed something and we are summarising on that?
And, we use ‘generally speaking’ even if that much of analysis is not went behind it?
Gray, I don’t know about the difference you propose. You conjecture that “broadly speaking” is used in some sort of conclusion, whereas “generally speaking” is not; but I don’t really perceive any meaningful difference in your examples. “Broadly speaking” does not have an undertone of conclusion for me any more than “generally speaking”. Both expressions may be used to introduce a conclusion, because a conclusion is often broader / more general than its arguments, that’s all.
I think the difference between the two is so subtle that it does not have any practical significance in this type of sentence.
A possible synonym:
-In general (means not precisely the same but close)
Cerberus, how many times did you right-click to synonyms in that response?