Did you want help, or not?
Also, if for any reason some day somewhere someone wants your opinion on design they'll probaby tell you the opinion you should have.
Not sure how to parse that. If somebody told me the opinion I should have, then it sounds like they don't want an opinion, and so I probably wouldn't give them one at all.
This is a place for mutual assistance. It is assumed that anyone posting an example would like feedback, and so I thought I'd point out that you are letting the browser resize your logo image, and it looks awful. Sorry you are so sensitive to the word "awful", but that's how it looks.
So...
... you could achieve a more aesthetic result by using a higher-resolution logo image or using a vector image format.
As well, it was initially the only thing I could see wrong with the site. I viewed it first on desktop, and both sites looked the same.
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Go look up "frame redirect". It's what you are doing on the second site. Don't do that, and I think your problem will go away.
"Frame redirects" are not real DNS redirects. They are used in cases, for example, where you are hosting on your home server, and you cannot have a permanent IP address (because of DHCP). They are also used for other situations where you cannot control the domain name. (For example, redirect to a blogging platform.)
There is no real DNS forwarding going on. A frame set is loaded from a web server, typically maintained by a hosting company, DNS provider, redirect service, etc. The content is loaded into a frame, and this effectively "hides" the real address of the website. the address the user sees in the address bar is the address of the redirect service server (which has DNS records directed to it) not the server that ultimately provides the content.
There are really two web servers involved here - one returns the frame set, and the second supplies the content. Redirect services usually gloss-over this fact, and misrepresent this as being similar to a DNS redirect. It is not. It's a trick that is appropriate for low-volume web sites, testing, etc. if your content will work well with it.
JQM doesn't live well in a frame set.
Edit: confirmed that the text is the correct size if you simply navigate directly to the real website that's being "masked" by the framed "redirect":
Maybe this is part of your client's marketing. Foreclosed? Have a drink!