Yes there is. In 2019 Boris would have comfortably beaten Corbyn in a UK presidential election.
No we would not have a President like Ireland either as they are a small nation not a permanent member of the UN Security Council, G7 and G20 like us, France and the USA, the latter 2 all of which have powerful elected Presidents like we would if we ended the monarchy.
The Irish President has no more power than our monarchs anyway, while having nowhere near the global name and brand recognition nor revenue brought in.
Of course you would, as you are an ideological republican