Names have been changed to protect the innocent ;).
"SEO ranking" can be very subjective...being in the SEO business like we are, your SEO expert should know better that the answer is never "site A's SEO is better than site B's SEO". It depends on what traffic you are going after, and the quality of that traffic. More doesn't necessarily equal better.
Putting aside his (and ours!) opinions on who's SEO is better, let's do a far more objective comparison:
varvy.com is a popular SEO tool. It identified several problems with www.yourfishinglodgesite.com that have a negative effect on the site's SEO that fishlodges.com does not have: display on mobile devices, security, no search engine sitemap, various page speed issues.
But what about an objective ranking comparison? In this business we often rely on various algorithms accessible via several online tools. Here, there's no single tool that will provide a completely definitive analysis, because they all do their analysis a bit different. So we usually use several of them and compound the results.
I ran your site through seoptimer.com it it was graded as a C+ overall, with a 67/100 as the SEO score. I ran fishlodges.com through the same tool, it was was graded B- overall, with a 90/100 SEO score.
Moving on, I then tried your site with site-analyzer.com, which received a 66 overall SEO score. With fishlodges.com it was 67.
Woorank, which is considered the most accurate and trustworthy by many professionals, was especially hard on both of our sites: 58.1/100 (your site) and 58.4 (our site).
What About Keywords?
The interesting thing about all these results is that I never told them what kind of visitors I'm hoping to attract to my site—what keywords I want to rank highly on. So what they're doing is assessing the SEO in general, on all aspects not related to specific keywords.
So I used upcity.com to analyze both of our sites on a keyword that we value, "fishing vacations". It does the usual SEO analysis but also factors in the keyword ranking. For that keyword, it assigned a score of 12 for us, twice the score it gave you (6). Our overall score was 67 (yours was 56).
Looking at the keyword analysis for your site, I know that you would rank better than us for keywords more specific to your operation, like "kenai river fishing".
Three conclusions here are: 1. There's no one "true" SEO ranking algorithm, 2. "Better" also depends on what you're using to measure "good" or "bad", like keywords (search terms). 3. Objectively speaking, your SEO expert may be hard-pressed to provide evidence to back up his opinion.
Not All Website Traffic Counts
You might also ask your SEO expert if, when reviewing your traffic, whether he filters out all spam traffic like we do (40% to 60% of all web traffic is not real). Most online advertisers, and many who are hired to increase web traffic don't filter this traffic out, so they report artificially high numbers to make their work seem better. We don't do that, so all our traffic is real (well almost—it's impossible to filter out 100%). There's an article here and here about this.
It's certainly not impossible that your site indeed does get more traffic currently, likely because it's been on the web longer than ours has. However, I would expect that 40% to 60% of that traffic is not real traffic, so doesn't count, and taking the bad traffic away, the traffic volumes are probably more similar.
And even if that's not the case, several objective sources confirm that our site has a stronger SEO position overall, which means that our rate of growth will be higher than yours, so at some point our "real" traffic will surpass your "real" traffic.
What Really Matters
But does it really matter who is right and wrong? I don't think so. Many of our current customers have excellent sites that rank well, some better than us on the keywords we pursue. They list with us simply because they want to easily extend their reach even farther, and obtain more leads than than they can on their own. For $255/year, we do that for a pretty reasonable price. To get the same results by improving your own site (to get those SEO scores—from above—higher) would cost you much more than several years of a listing on fishlodges.com.
We drive more traffic to a lodge's own website, and because we make it more efficient for our visitors to find the ideal vacation for them up front by answering more questions up front, the leads coming to you are less tire-kickers, and more people ready to book (i.e. it is very good traffic).
I ended the email by apologizing for such a lengthy reply...being an SEO guy myself, I get a bit charged up when other professionals spew opinions that are not backed up by facts, usually out of just trying to protect their own positions.