I'm somewhere in-between on this one. On one hand, I don't really think that the two of them are extremely different in their political beliefs. From what I've seen of the two, I highly doubt that Obama is anywhere near as liberal as he wants his fan-base to think he is. Similarly, I don't believe that Romney is anywhere near as conservative as he tried to look during the 2012 election. Obama has constantly tried to look like an extremist liberal while running for office in order to appeal to the young crowd that wants change. Romney was trying to look like a conservative, religious zealot to appeal to the far right. When in office though, neither seem to act at the same level of extremity as they campaigned on. So, if Romney was elected, I highly doubt that the overarching policy decisions made by the US would be all that different.
The difference in my eyes really would have taken place in one of two occasions. The first one would be the crisis of Crimea. While I don't think Romney would have used a full out assault as someone like McCain might have, I have a feeling he would have approached Russia much more aggressively. The second one would be the policies that they try to leave the White House with. Obama has been pushing for his liberal agenda, whereas Romney likely would have pushed for his conservative one. It is unlikely though that these two agendas would be too radically different for the aforementioned reasons.
I like how people are trashing Romney yet he established successful healthcare in his state. He took a left wing policy and made it work. It concerns me that you would rather have a liar than someone who wanted job security, increased wages, lower taxes , extended tax brackets, and healthcare based off his successful model.